Mark Noble's controversial early penalty set West Ham on their way to a comfortable victory which consigned Norwich to a fourth consecutive defeat.
Noble calmly found the corner after three minutes when Ryan Bennett was deemed to have held down Winston Reid.
Norwich almost levelled when a Robert Snodgrass free-kick hit the post but Joey O'Brien's shot made it 2-0.
The hosts were largely untroubled after the break and secured the win despite Russell Martin's 90th-minute strike.
Defender Martin's third goal in two games produced a nervy finale, but could not prevent the Hammers leapfrogging their visitors and moving up to 11th place in the Premier League table.
West Ham's 20-year wait
West Ham's last league win over Norwich before today was in April 1992 - although they have since won home and away in FA Cup ties in 2005 and 2006 respectively.
The margin of victory - just
West Ham's second in nine games
- could have been far greater with Canaries goalkeeper Mark Bunn having to make several superb saves and the hosts also wasting a couple of glorious opportunities.
But Norwich will point to the harsh second-minute penalty award as the catalyst for their demise.
Three defeats in a row over Christmas had marred a 10-game unbeaten run for Norwich.
And although all three of those losses were against sides in the top seven -
including Manchester City
and Chelsea - the last thing their fragile confidence needed was to be chasing the game within three minutes. But like the home reverse against City, that is exactly what happened.
Their normally calm manager Chris Hughton was furious and bemused in equal measure as referee Mark Clattenburg penalised Bennett for grabbing Reid's shirt as a looping ball was played into the box.
Reid seemed to be impeding Bennett just as as much but Noble ignored the protests and stayed cool to convert the spot-kick and put the hosts ahead.
Hughton critical of penalty decision
Norwich refused to be rattled, but a side deprived of both injured main strikers Grant Holt and Steve Morison struggled to create chances.
Despite a willing display from on-loan Tottenham teenager Harry Kane, they lacked punch and presence up front and West Ham cleverly stifled the main creative threat from the ever-lively Wes Hoolahan.
Snodgrass was desperately unlucky with a brilliant 20-yard free-kick that hit the post with the score at 1-0, and they appealed for penalties of their own when the ball hit Reid on the arm, and then after the break when Kane tumbled in the box under a challenge from James Tomkins.
But West Ham, with Noble in dominant form and midfield partner Jack Collison equally impressive on his first start this season, played with a greater tempo and created the majority of the chances.
Bunn pulled off a breathtaking one-handed reaction stop to keep out Collison's effort just before the hosts made it 2-0 when O'Brien continued his run into the box to sidefoot home from 10 yards after great work by Noble.
Norwich appealed for a foul by Carlton Cole on Alex Tettey in the build up but Clattenburg waved play on, much to Hughton's disgust.
Martin FisherMatch of the Day commentator
The visitors will feel they have every reason to complain about referee Mark Clattenburg's decision to award an early penalty but West Ham had the better chances and could easily have won by more. Norwich managed to hang on for 2-0 at half-time but could not find a way back into the game after the break and slip to a fourth successive defeat.
Matthew Taylor's fierce 20-yard strike then forced a save from Bunn before the otherwise impressive Cole produced a terrible miss when he somehow skied the ball over the bar from three yards after a fabulous move on the right involving Noble and Guy Demel.
West Ham sat deeper after the break and Norwich saw much more of the ball but were still unable to create much.
Kane appealed hopefully after tumbling when racing through on goal while at the other end the Hammers almost added a third goal when Ricardo Vaz Te's header hit the post.
But West Ham did not need the security of a third despite Martin pulling a goal back with just over 30 seconds of normal time remaining when he did brilliantly to volley into the corner of the net from substitute Elliott Bennett's right-wing cross.
West Ham manager Sam Allardyce:
"I was wondering if we were going to hold our confidence and performance level at home. It has been really good even though we have had two back-to-back defeats. They showed they have the mentality to cope with whatever is thrown at them.
"We are glad that their goal didn't come a bit earlier but it's a shame the score did not reflect how well we played. We should have scored a few more and and we did it with really good football. We deserved the win.
Allardyce pleased to end "torturous" run
"Often in a crowded penalty box it is impossible to give penalties like that, but I could see it from where I was in the dugout. That early goal gave us the confidence to go on.
"The disappointing thing was the chances the front lads missed, with balls just flashing across the box needed a tap in.
"We lost a goal in the 90th minute which made us edgy in the end when we should have been out of sight. We will continue to try to brush up on our finishing techniques with the lads and hope the next time round we are more clinical with our finishing."
Norwich City boss Chris Hughton:
"The key decisions in the game did not go in our favour, but we did not start well enough.
"We accept Ryan Bennett had hold of the lad's shirt, but I also saw Reid's forearm in Ryan's chest. They are very close, he is not pulling Reid so he cannot get away, it is something you see game in and game out right throughout the country.
"On almost every occasion you do not see a penalty, particularly when it is so early in the game, so I was very surprised when he gave it.
"I also don't accept it was not a foul on Alex Tettey leading up to the second goal and certainly was a handball in the first half and then the incident on Harry Kane. We have been on the end of poor decisions.
"We showed in the second half a bit more of what we are about. Nobody has really given us a beating and they have all been really close games. We have to be at our best to get results and we have been close in the last four games."
90:00+3:52 The referee blows for the end of the match.
90:00+3:21 Anthony Pilkington produces a left-footed shot from the edge of the box and misses to the right of the target.
90:00+1:23 The offside flag is raised against Simeon Jackson. Jussi Jaaskelainen takes the indirect free kick.
90:00+0:42 Unfair challenge on Russell Martin by James Tomkins results in a free kick. David Fox takes the direct free kick.
89:27 Simeon Jackson sends in a cross,
89:20 Simeon Jackson provided the assist for the goal.
89:20 GOAL - Russell Martin:West Ham 2 - 1 Norwich Russell Martin finds the net with a goal from inside the box to the bottom right corner of the goal. West Ham 2-1 Norwich.
88:30 The ball is delivered by Russell Martin, clearance by James Tomkins.
87:03 Modibo Maiga challenges Sebastien Bassong unfairly and gives away a free kick. Mark Bunn takes the free kick.
Correction - 84:06 Substitution (West Ham) makes a substitution, with Jordan Spence coming on for Matthew Jarvis.
Correction - 84:06 Outswinging corner taken left-footed by Robert Snodgrass played to the near post. Effort on goal by David Fox from long distance
goes over the crossbar.
84:06 Substitution Matthew Jarvis goes off and Jordan Spence comes on.
84:06 Corner taken by Robert Snodgrass from the left by-line played to the near post. Effort on goal by Russell Martin from a long
way out goes over the bar.
83:36 Robert Snodgrass fouled by Matthew Taylor, the ref awards a free kick. Russell Martin restarts play with the free kick.
82:22 Carlton Cole produces a header from deep inside the six-yard box which goes wide of the right-hand post.
82:22 Substitution David Fox replaces Jonathan Howson.
82:22 Outswinging corner taken from the right by-line by Mark Noble,
81:38 Substitution Modibo Maiga joins the action as a substitute, replacing Ricardo Vaz Te.
78:13 Shot by Alexander Tettey from a long way out goes over the net.
77:59 The ball is crossed by Elliott Bennett, Jack Collison manages to make a clearance.
77:30 The ball is swung over by Gary O'Neil, Robert Snodgrass manages to make a clearance.
74:51 Corner taken left-footed by Robert Snodgrass to the near post, Carlton Cole makes a clearance.
71:42 Shot by Robert Snodgrass. Save by Jussi Jaaskelainen.
70:06 Substitution Joey O'Brien goes off and Gary O'Neil comes on.
69:16 Substitution (Norwich) makes a substitution, with Elliott Bennett coming on for Wesley Hoolahan.
69:16 Substitution Simeon Jackson replaces Harry Kane.
Correction - 67:54 Corner taken by Robert Snodgrass, Michael Turner produces a header from close range which goes wide of the left-hand upright.
67:54 Corner taken by Robert Snodgrass from the right by-line, Michael Turner has a headed effort at goal from close range which
goes wide of the left-hand post.
67:00 Ricardo Vaz Te takes a shot. Sebastien Bassong gets a block in.
65:27 Russell Martin is penalised for handball and concedes a free kick. Strike on goal comes in from Matthew Taylor from the free
kick, blocked by Anthony Pilkington.
63:51 Matthew Taylor sends in a cross, Header from close range by Ricardo Vaz Te bounces off the post.
62:48 Handball decision goes against Jack Collison. Direct free kick taken by Alexander Tettey.
61:27 Mark Noble takes a shot. Sebastien Bassong gets a block in. Corner from right by-line taken by Matthew Taylor.
61:12 Matthew Jarvis produces a cross, Sebastien Bassong manages to make a clearance.
60:43 Anthony Pilkington delivers the ball, Winston Reid makes a clearance.
60:25 The ball is crossed by Jack Collison, clearance made by Russell Martin.
57:45 A cross is delivered by Ricardo Vaz Te.
57:24 Ricardo Vaz Te produces a cross, clearance by Ryan Bennett.
55:46 Matthew Taylor takes the inswinging corner, Russell Martin makes a clearance. Inswinging corner taken by Matthew Taylor from
the right by-line, James Tomkins has a headed effort at goal from close in which goes wide of the left-hand upright.
55:12 Harry Kane is ruled offside. Free kick taken by James Tomkins.
53:20 Mark Noble delivers the ball, clearance made by Sebastien Bassong.
52:40 The referee blows for offside. Jussi Jaaskelainen restarts play with the free kick.
51:04 Unfair challenge on Matthew Jarvis by Ryan Bennett results in a free kick. Mark Noble takes the direct free kick.
49:49 The ball is delivered by Jack Collison.
48:32 The ball is delivered by Ricardo Vaz Te, clearance made by Sebastien Bassong.
47:53 Handball by Carlton Cole. Direct free kick taken by Mark Bunn.
46:48 Robert Snodgrass fouled by Joey O'Brien, the ref awards a free kick. Free kick crossed left-footed by Robert Snodgrass. Michael
Turner is flagged offside by the assistant referee. Free kick taken by Jussi Jaaskelainen.
46:03 Corner taken by Mark Noble from the right by-line played to the near post, Winston Reid takes a shot.
Correction - 45:59 Corner taken by Mark Noble from the right by-line to the near post, Winston Reid takes a shot.
45:34 The ball is swung over by Matthew Taylor.
45:01 The match restarts for the second half.
45:00+2:08 The referee blows for half time.
45:00+1:12 Harry Kane is penalised for handball and concedes a free kick. Free kick taken by Mark Noble.
45:00+0:42 Jonathan Howson takes a shot. Blocked by Winston Reid.
44:34 Effort from deep inside the area by Ricardo Vaz Te misses to the right of the goal.
43:50 Mark Noble takes a shot. Jonathan Howson gets a block in. Inswinging corner taken by Mark Noble from the left by-line played
to the near post, clearance by Harry Kane.
41:36 Centre by Matthew Taylor, clearance made by Russell Martin. Inswinging corner taken left-footed by Matthew Taylor from the
right by-line to the near post, Russell Martin manages to make a clearance. Corner from the right by-line taken by Matthew
Taylor, Carlton Cole challenges Mark Bunn unfairly and gives away a free kick. Mark Bunn takes the direct free kick.
40:39 Unfair challenge on Harry Kane by Mark Noble results in a free kick. Robert Snodgrass restarts play with the free kick.
40:08 Robert Snodgrass fouled by Carlton Cole, the ref awards a free kick. Mark Bunn restarts play with the free kick.
37:48 The referee blows for offside. Free kick taken by Joey O'Brien.
36:09 Alexander Tettey fouled by Carlton Cole, the ref awards a free kick. Direct free kick taken by Michael Turner.
35:21 Carlton Cole produces a left-footed shot from inside the six-yard box that clears the bar.
34:34 Mark Noble delivers the ball, clearance made by Michael Turner.
30:51 Effort on goal by Matthew Taylor from 20 yards. Save made by Mark Bunn. Corner from the left by-line taken by Mark Noble,
Jack Collison concedes a free kick for a foul on Michael Turner. Free kick taken by Mark Bunn.
30:21 The ball is crossed by Matthew Jarvis, Robert Snodgrass manages to make a clearance. Short corner worked by Mark Noble.
Correction - 25:01 GOAL - Joey O'Brien:West Ham 2 - 0 Norwich Goal scored by Joey O'Brien from close in to the bottom left corner of the goal. West Ham 2-0 Norwich.
25:01 Assist on the goal came from Mark Noble.
25:01 GOAL - Joey O'Brien:West Ham 2 - 0 Norwich Joey O'Brien finds the net with a goal from close in to the bottom left corner of the goal. West Ham 2-0 Norwich.
23:29 Guy Demel produces a cross, Jack Collison takes a shot. Save made by Mark Bunn.
22:55 Ricardo Vaz Te challenges Sebastien Bassong unfairly and gives away a free kick. Mark Bunn takes the free kick.
21:52 Russell Martin concedes a free kick for a foul on Ricardo Vaz Te. Joey O'Brien takes the direct free kick.
21:00 Anthony Pilkington produces a left-footed shot from just outside the box that goes wide right of the goal.
19:23 Jack Collison handles the ball and concedes a free kick. Robert Snodgrass has a direct shot on goal from the free kick.
18:38 Matthew Jarvis delivers the ball, free kick awarded for a foul by Carlton Cole on Russell Martin. Free kick taken by Mark
17:22 Free kick awarded for a foul by Wesley Hoolahan on James Tomkins. Free kick taken by Jussi Jaaskelainen.
16:37 The official flags Ricardo Vaz Te offside. Mark Bunn takes the free kick.
16:13 The ball is delivered by Matthew Jarvis, clearance made by Robert Snodgrass.
15:57 Robert Snodgrass gives away a free kick for an unfair challenge on Joey O'Brien. Direct free kick taken by Mark Noble.
14:44 A cross is delivered by Carlton Cole, clearance by Jonathan Howson.
13:53 Unfair challenge on Winston Reid by Harry Kane results in a free kick. Jussi Jaaskelainen takes the free kick.
13:33 Matthew Taylor sends in a cross, Russell Martin manages to make a clearance.
12:49 Effort on goal by Carlton Cole from 20 yards. Save by Mark Bunn.
8:12 Unfair challenge on Alexander Tettey by Carlton Cole results in a free kick. Mark Bunn takes the direct free kick.
5:49 Robert Snodgrass sends in a cross, clearance made by James Tomkins.
5:23 Jack Collison gives away a free kick for an unfair challenge on Harry Kane. Direct free kick taken by Sebastien Bassong.
4:29 Free kick awarded for a foul by Carlton Cole on Alexander Tettey. Michael Turner takes the direct free kick.
2:29 Assist on the goal came from Winston Reid.
2:29 GOAL - Mark Noble:West Ham 1 - 0 Norwich Mark Noble scores a power penalty. West Ham 1-0 Norwich.
1:22 Penalty awarded for an unfair challenge on Winston Reid by Ryan Bennett.
0:54 Inswinging corner taken right-footed by Mark Noble, Mark Bunn makes a save.
0:33 Unfair challenge on Carlton Cole by Michael Turner results in a free kick. Direct free kick taken by Mark Noble.
0:00 The referee gets the match started.
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