Ten-man Manchester City held off a determined Norwich to win a pulsating game at Carrow Road.
City surged ahead when Edin Dzeko twice slotted home in the first four minutes.
Anthony Pilkington's free-kick gave Norwich hope but, despite the visitors having Samir Nasri sent off, Sergio Aguero added a third for the champions.
Mancini bemused by Nasri red card
Norwich's Russell Martin scored twice either side of a Dzeko shot that went in off the post and keeper Mark Bunn, as the visitors clung on for victory.
The champions, beaten at Sunderland on Boxing Day, were made to demonstrate their appetite to retain their Premier League title with a victory achieved despite the handicap of losing Nasri to a straight red card on the stroke of half-time.
The French winger and Sebastian Bassong squared up to each other after a strong tackle from the latter took both the ball and Nasri, who reacted angrily and appeared to flick his head towards the Canaries defender - though the visitors were clearly aggrieved at what they regarded as a very harsh decision.
The talk following the shock defeat at the Stadium of Light had all been about Manchester City's misfiring strikeforce, and their forwards seemed to have taken the criticism to heart judging by the rampant start at Carrow Road.
Steve WilsonBBC Match of the Day commentator
"Manchester City were given a huge scare by Norwich City but they have passed a big test at Carrow Road. They clung on for the win and what a way to sign off 2012 and what a match."
The first goal was beautifully worked as Aguero picked out David Silva on the edge of the area and he slipped a first-time pass to Dzeko, who sent a shot into the bottom corner.
Norwich barely had time to regroup before their opponents added a second.
Canaries keeper Bunn was tempted out of his goal in an unsuccessful attempt to close down Aguero, who laid the ball back for Dzeko to slot into an empty net.
Norwich complained about a challenge from Vincent Kompany on Bradley Johnson in the build-up to the goal but it was allowed to stand.
The visitors were then almost gifted a third when home defender Javier Garrido's poor backpass was tipped over the crossbar by a backtracking Bunn.
But the Canaries have beaten Arsenal and Manchester United at Carrow Road this season and they responded with Pilkington's 20-yard free-kick, which found the net via a deflection off Gael Clichy.
Norwich character pleases Hughton
Down to 10 men, Roberto Mancini's side restored their two-goal lead after half-time when Aguero raced on to a Yaya Toure ball before classily dinking the ball over Bunn.
But the home side pressed forward undeterred, Jonathan Howson having a shot palmed wide by keeper Joe Hart.
From the resulting corner, a Robert Snodgrass cross was nodded back across goal by Bassong and Martin was on hand to guide in a header and reduce the deficit to one again.
The visitors might have thought they had put the match out of reach when Dzeko's fierce drive came back off the post and hit keeper Bunn on its way into the net but Norwich were still not finished, Martin grabbing his second when he diverted a Bradley Johnson shot into the net following a goalmouth scramble after 75 minutes.
Mancini's men managed to keep Norwich at bay for the remainder of the game and remain seven points adrift of leaders Manchester United in second.
Norwich manager Chris Hughton:
"Manchester City showed why they spend the amount of money they do for the offensive players they have, but you can't be 2-0 down so early on and expect to have a good day.
"However, we displayed great character and certainly at 4-3 it seemed it might be going our way, but again they showed real good quality.
"I cannot fault the endeavour of the players we have got, so now we will look to go again."
90:00+5:14 Free kick awarded for a foul by Simeon Jackson on Gareth Barry. Joe Hart restarts play with the free kick.
90:00+4:35 Robert Snodgrass produces a cross, save by Joe Hart.
90:00+4:04 Sebastien Bassong takes a shot. Blocked by Vincent Kompany.
90:00+2:11 Joe Hart takes the free kick.
90:00+2:11 Substitution Francisco Javi Garcia comes on in place of Sergio Aguero.
90:00+2:11 Free kick awarded for a foul by Simeon Jackson on Joleon Lescott.
90:00+1:52 Sergio Aguero takes a shot. Brilliant save by Mark Bunn.
90:00+1:20 Robert Snodgrass fouled by Matija Nastasic, the ref awards a free kick. Free kick crossed by Robert Snodgrass, clearance by
88:59 Centre by Simeon Jackson.
87:42 Javier Garrido challenges James Milner unfairly and gives away a free kick. Direct free kick taken by James Milner.
85:09 Vincent Kompany concedes a free kick for a foul on Simeon Jackson. The ball is delivered by Javier Garrido, Effort from inside
the area by Michael Turner misses to the right of the target.
84:02 Vincent Kompany challenges Harry Kane unfairly and gives away a free kick. Free kick crossed by Robert Snodgrass, Gael Clichy
manages to make a clearance.
82:48 Corner taken right-footed by James Milner from the right by-line, Foul by Joleon Lescott on Sebastien Bassong, free kick awarded.
Direct free kick taken by Mark Bunn.
82:48 Booking Anthony Pilkington is cautioned.
82:25 Sergio Aguero takes a shot. Save made by Mark Bunn.
80:31 Substitution Joleon Lescott comes on in place of Edin Dzeko.
74:31 Bradley Johnson provided the assist for the goal.
74:31 GOAL - Russell Martin:Norwich 3 - 4 Man City Russell Martin finds the back of the net with a goal from close in high into the middle of the goal. Norwich 3-4 Man City.
Correction - 74:23 Inswinging corner taken left-footed by Robert Snodgrass, Harry Kane takes a shot. Blocked by Matija Nastasic. Bradley Johnson
has an effort at goal.
74:23 Corner taken left-footed by Robert Snodgrass, Harry Kane takes a shot. Blocked by Matija Nastasic. Volleyed shot by Bradley
73:43 Substitution Simeon Jackson is brought on as a substitute for Wesley Hoolahan.
72:31 Free kick awarded for a foul by Anthony Pilkington on James Milner. Joe Hart takes the direct free kick.
71:42 The ball is delivered by Yaya Toure, clearance by Michael Turner.
70:52 A cross is delivered by Jonathan Howson, clearance by Vincent Kompany.
70:22 Corner taken by Anthony Pilkington, Matija Nastasic makes a clearance.
69:51 Corner taken left-footed by Robert Snodgrass, clearance by Pablo Zabaleta.
69:02 Sergio Aguero produces a right-footed shot from close range which goes wide of the right-hand post.
66:16 Edin Dzeko provided the assist for the goal.
66:16 GOAL - Mark Bunn:Norwich 2 - 4 Man City Own goal by Mark Bunn. Norwich 2-4 Man City.
66:16 Shot by Edin Dzeko from deep inside the area bounces off the post.
64:43 Robert Snodgrass produces a left-footed shot from just outside the box that misses to the right of the target.
62:33 Sebastien Bassong provided the assist for the goal.
62:33 GOAL - Russell Martin:Norwich 2 - 3 Man City Russell Martin finds the net with a headed goal from inside the area. Norwich 2-3 Man City.
62:30 Short corner worked by Robert Snodgrass. Robert Snodgrass delivers the ball.
62:17 Jonathan Howson takes a shot. Joe Hart makes a save.
62:08 The ball is sent over by Javier Garrido, clearance by Matija Nastasic.
61:17 The ball is swung over by Javier Garrido, clearance by Gareth Barry.
60:49 Robert Snodgrass sends in a cross, Joe Hart makes a save.
59:53 Sergio Aguero takes a shot. Save by Mark Bunn.
58:56 Harry Kane takes a shot. Blocked by Pablo Zabaleta.
58:04 Anthony Pilkington sends in a cross, Header by Robert Snodgrass from deep inside the penalty area misses to the right of the
57:51 Jonathan Howson crosses the ball, Pablo Zabaleta makes a clearance.
57:13 Unfair challenge on Robert Snodgrass by Sergio Aguero results in a free kick. The free kick is delivered left-footed by Robert
Snodgrass from right channel, Pablo Zabaleta makes a clearance.
55:40 Substitution Alexander Tettey leaves the field to be replaced by Jonathan Howson.
55:40 Substitution (Man City) makes a substitution, with James Milner coming on for David Silva.
53:55 Outswinging corner taken left-footed by David Silva played to the near post, Robert Snodgrass makes a clearance.
53:05 Yaya Toure takes a shot. Alexander Tettey makes a clearance. Corner taken by David Silva played to the near post, clearance
made by Sebastien Bassong.
51:44 Russell Martin delivers the ball, save made by Joe Hart.
51:01 Booking Caution for Bradley Johnson.
49:27 Yaya Toure provided the assist for the goal.
49:27 GOAL - Sergio Aguero:Norwich 1 - 3 Man City Goal scored by Sergio Aguero from close in low into the middle of the goal. Norwich 1-3 Man City.
48:50 Shot from 20 yards by Anthony Pilkington. Pablo Zabaleta gets a block in.
48:06 Free kick awarded for a foul by Yaya Toure on Harry Kane. Robert Snodgrass crosses the ball from the free kick left-footed
from right channel, Pablo Zabaleta makes a clearance.
47:54 Robert Snodgrass produces a cross, Vincent Kompany manages to make a clearance.
45:36 Outswinging corner taken from the right by-line by Sergio Aguero.
45:01 The referee starts the second half.
45:00+3:08 The ref blows to signal half-time.
45:00+2:36 The ball is delivered by Anthony Pilkington, save made by Joe Hart.
45:00+0:35 The ball is sent over by Harry Kane, Matija Nastasic makes a clearance.
45:00+0:23 The ball is delivered by Anthony Pilkington, Vincent Kompany manages to make a clearance.
43:15 Pablo Zabaleta restarts play with the free kick.
43:15 Substitution Harry Kane on for Steve Morison.
43:15 Sent off Samir Nasri shown a red card for violent conduct.
43:00 Booking Sebastien Bassong booked.
42:29 Foul by Sebastien Bassong on Samir Nasri, free kick awarded.
39:50 Effort from outside the penalty box by Yaya Toure goes wide left of the goal.
39:12 Free kick awarded for an unfair challenge on Matija Nastasic by Steve Morison. Free kick taken by Matija Nastasic.
36:41 Shot by Edin Dzeko. Blocked by Bradley Johnson.
35:29 Foul by Alexander Tettey on Gareth Barry, free kick awarded. Yaya Toure takes the free kick.
34:29 Outswinging corner taken by Samir Nasri from the right by-line played to the near post, Vincent Kompany takes a shot. Blocked
by Robert Snodgrass.
34:13 The ball is delivered by Yaya Toure, Bradley Johnson manages to make a clearance.
31:03 Sergio Aguero gives away a free kick for an unfair challenge on Alexander Tettey. Mark Bunn restarts play with the free kick.
30:40 The ball is delivered by Robert Snodgrass, clearance by Gael Clichy.
30:01 The ball is swung over by Steve Morison.
25:13 Yaya Toure concedes a free kick for a foul on Wesley Hoolahan. Direct free kick taken by Michael Turner.
24:49 Corner taken right-footed by Samir Nasri from the right by-line, Russell Martin makes a clearance.
24:39 Centre by Samir Nasri, clearance made by Bradley Johnson.
23:47 Corner taken by Samir Nasri, clearance made by Michael Turner. The ball is swung over by Gael Clichy, Michael Turner manages
to make a clearance.
21:15 A cross is delivered by Samir Nasri, clearance made by Michael Turner.
18:30 Robert Snodgrass has an effort at goal from outside the box which goes wide left of the target.
17:52 Robert Snodgrass crosses the ball in from the free kick, Edin Dzeko manages to make a clearance.
17:52 Booking The referee shows Gael Clichy a yellow card.
17:45 Gael Clichy gives away a free kick for an unfair challenge on Robert Snodgrass.
16:35 The ball is sent over by Steve Morison, clearance by Matija Nastasic.
16:11 Centre by Samir Nasri, save by Mark Bunn.
14:02 Assist on the goal came from Robert Snodgrass.
14:02 GOAL - Anthony Pilkington:Norwich 1 - 2 Man City Anthony Pilkington scores a goal direct from the free kick from just outside the penalty area low into the middle of the goal.
Norwich 1-2 Man City.
13:09 Free kick awarded for an unfair challenge on Robert Snodgrass by Vincent Kompany.
12:53 Steve Morison crosses the ball.
11:21 Sergio Aguero produces a right-footed shot from just outside the box that misses to the right of the net.
10:11 The ball is crossed by Pablo Zabaleta, Javier Garrido makes a clearance. Corner taken by Samir Nasri from the right by-line
to the near post, Robert Snodgrass manages to make a clearance.
7:51 The ball is swung over by Anthony Pilkington, save by Joe Hart.
7:10 The ball is delivered by Gareth Barry, clearance made by Russell Martin. David Silva takes a outswinging corner to the near
post, clearance made by Robert Snodgrass.
6:25 Foul by Bradley Johnson on David Silva, free kick awarded. Direct free kick taken by Gareth Barry.
5:17 The assistant referee signals for offside against Steve Morison. Gael Clichy takes the direct free kick.
4:00 Assist on the goal came from Sergio Aguero.
4:00 GOAL - Edin Dzeko:Norwich 0 - 2 Man City Edin Dzeko gets on the score sheet with a goal from inside the box to the bottom left corner of the goal. Norwich 0-2 Man
1:20 Assist by David Silva.
1:20 GOAL - Edin Dzeko:Norwich 0 - 1 Man City Edin Dzeko gets on the score sheet with a goal from inside the penalty area to the bottom left corner of the goal. Norwich
0-1 Man City.
0:18 The ball is delivered by Gael Clichy, Javier Garrido makes a clearance.
0:00 The game gets underway.
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