Bristol City came into the game having conceded more goals than any other side in the division and goalkeeper Tom Heaton pulled off a superb save at the start to keep out Jacobs' shot from a corner.
Sam Baldock and Albert Adomah then went close for the hosts before they conceded the 44th and 45th goals of their season to Hendrick and Bryson.
Stung by going behind, Robins manager Derek McInnes brought on top scorer Steve Davies at the interval as he sought to end an eight-game winless run at Ashton Gate which stretches back to 25 August.
The decision ultimately went without reward, but the Scottish striker twice went close to scoring with a header from an Adomah corner and a 20-yard curling effort which was saved well by goalkeeper Adam Legzdins.
The loss saw McInnes' men remain one spot outside the relegation positions but level on points with 22nd-placed Barnsley.
Bristol City manager Derek McInnes:
"It doesn't matter what formation you employ if you fail to defend crosses as we did for Derby's two goals.
"We also have a problem at the moment with being vulnerable after we concede.
"By taking their chances, Derby earned the right to get 11 men behind the ball in the second half and that made it very difficult for us.
"If we had taken our chances it would have been a different story. Liam Fontaine and Sam Baldock should have scored and there were other opportunities."
Derby boss Nigel Clough:
"We know that if we are to get where we want to be this season our away form has to improve, so this was a huge result.
"Bristol have been struggling at home, but they are still a dangerous side with some terrific away wins to prove that, we took our chances and then kept the ball well to kill off the game, so all credit to the players.
"Our aim remains as it was at the start of the season - to be a top-half team and see where that takes us.
"A clean sheet was a bonus because we haven't had too many of those and overall I'm very happy with the performance."
Live text and stats
Saturday, 15 December 2012
26 Bryan (Stead 71)
39 Bates (Cunningham 44)
18 Taylor (Davies 46 yellow card)
15 O'Brien (Freeman 87)
04 Bryson (Davies 68)
07 Coutts yellow card
08 Hendrick yellow card
19 Hughes (O'Connor 90)
Ref: D'UrsoAtt: 12,526
Attempts on target
Attempts off target
95:11 The final whistle is blown by the referee.
90:00+1:02 Sam Baldock has an effort at goal from deep inside the area missing to the left of the target.
90:00+0:05 Free kick awarded for a foul by Steven Davies on Jeff Hendrick. Jeff Hendrick restarts play with the free kick.
89:10 Substitution James O'Connor comes on in place of Will Hughes.
88:18 Albert Adomah takes a shot. Adam Legzdins makes a fantastic save. Corner taken by Albert Adomah, Marvin Elliott takes a shot.
Save by Adam Legzdins.
86:40 Substitution Mark O'Brien goes off and Kieron Freeman comes on.
85:52 Jon Stead takes a shot. Save made by Adam Legzdins.
83:30 The assistant referee flags for offside against Ben Davies. Tom Heaton takes the indirect free kick.
82:16 Paul Coutts produces a right-footed shot from just outside the penalty box that misses to the left of the target.
75:42 Effort on goal by Sam Baldock from just inside the penalty area goes harmlessly over the target.
74:55 Liam Fontaine takes a shot. Brilliant save by Adam Legzdins. Corner taken by Jon Stead from the left by-line to the near post,
Jeff Hendrick makes a clearance.
74:18 Shot by Steven Davies from 20 yards. Save by Adam Legzdins. Inswinging corner taken from the left by-line by Jon Stead, clearance
made by Richard Keogh.
72:09 Richard Keogh takes a shot. Tom Heaton makes a comfortable save.
71:34 Gareth Roberts takes a shot. Blocked by Liam Fontaine. Corner from the left by-line taken by Michael Jacobs, save made by
70:17 Paul Coutts takes the free kick.
70:17 Substitution Jon Stead joins the action as a substitute, replacing Joe Bryan.
70:17 Free kick awarded for an unfair challenge on Ben Davies by Joe Bryan.
68:07 Corner taken right-footed by Albert Adomah from the right by-line, Header by Steven Davies from deep inside the penalty area
misses to the left of the target.
66:03 Outswinging corner taken from the right by-line by Jeff Hendrick.
66:03 Substitution Craig Bryson leaves the field to be replaced by Ben Davies.
66:03 Michael Jacobs takes a shot. Stephen McManus gets a block in.
64:15 Unfair challenge on Conor Sammon by Greg Cunningham results in a free kick. John Brayford takes the direct free kick.
63:38 Unfair challenge on Albert Adomah by Will Hughes results in a free kick. Greg Cunningham restarts play with the free kick.
60:19 Stephen McManus takes the free kick.
60:19 Booking Jeff Hendrick goes into the referee's book for unsporting behaviour.
60:12 Free kick awarded for a foul by Jeff Hendrick on Albert Adomah.
55:49 Free kick taken by Richard Keogh.
55:49 Booking The referee books Steven Davies for unsporting behaviour.
55:21 Will Hughes fouled by Neil Danns, the ref awards a free kick.
54:52 Will Hughes gives away a free kick for an unfair challenge on Neil Danns. Stephen McManus takes the free kick.
51:00 Michael Jacobs takes a inswinging corner from the left by-line played to the near post, clearance made by Stephen McManus.
49:51 Marvin Elliott fouled by Conor Sammon, the ref awards a free kick. Direct free kick taken by Albert Adomah.
46:58 Free kick crossed left-footed by Greg Cunningham from left wing, John Brayford manages to make a clearance.
46:58 Booking The referee books Paul Coutts for unsporting behaviour.
46:41 Free kick awarded for an unfair challenge on Greg Cunningham by Paul Coutts.
45:01 The second half begins.
45:01 Substitution Ryan Taylor leaves the field to be replaced by Steven Davies.
45:00+2:12 The ref blows to signal half-time.
44:24 Unfair challenge on Ryan Taylor by Jeff Hendrick results in a free kick. Richard Foster delivers the ball from the free kick
right-footed from right channel, clearance by Richard Keogh.
43:06 Jeff Hendrick takes the direct free kick.
43:06 Substitution (Bristol City) makes a substitution, with Greg Cunningham coming on for Matthew Bates.
43:06 Jeff Hendrick fouled by Ryan Taylor, the ref awards a free kick.
42:17 Free kick awarded for a foul by Conor Sammon on Richard Foster. The free kick is swung in right-footed by Albert Adomah,
Paul Coutts manages to make a clearance.
39:22 John Brayford has an effort at goal from outside the area which goes wide left of the target.
37:57 Sam Baldock takes a shot. Save made by Adam Legzdins. Foul by Ryan Taylor on Gareth Roberts, free kick awarded. Direct free
kick taken by Adam Legzdins.
Correction - 37:01 Effort on goal by Sam Baldock from just inside the box goes harmlessly over the target.
37:01 Paul Coutts takes a shot from just inside the penalty box which clears the bar.
35:48 The assist for the goal came from Gareth Roberts.
35:48 GOAL - Craig Bryson:Bristol City 0 - 2 Derby Craig Bryson grabs a headed goal from close in. Bristol City 0-2 Derby.
35:25 Neil Danns challenges Michael Jacobs unfairly and gives away a free kick. Jeff Hendrick takes the free kick.
33:04 Assist on the goal came from Michael Jacobs.
33:04 GOAL - Jeff Hendrick:Bristol City 0 - 1 Derby Goal scored by Jeff Hendrick from close in to the bottom left corner of the goal. Bristol City 0-1 Derby.
26:40 Effort on goal by Paul Coutts from just inside the penalty area goes over the target.
22:35 Michael Jacobs takes a inswinging corner to the near post, clearance made by Richard Foster.
19:28 The ball is delivered by Albert Adomah, save by Adam Legzdins.
18:01 Shot from deep inside the area by Joe Bryan clears the crossbar.
17:11 Paul Coutts takes a shot. Save made by Tom Heaton.
16:12 Foul by Ryan Taylor on Richard Keogh, free kick awarded. Free kick taken by Adam Legzdins.
13:16 Sam Baldock takes a shot. Adam Legzdins makes a save.
9:08 Mark O'Brien challenges Ryan Taylor unfairly and gives away a free kick. The free kick is delivered right-footed by Albert
Adomah from right channel.
5:33 Short corner taken by Paul Coutts, Michael Jacobs takes a shot. Save made by Tom Heaton. Corner taken by Will Hughes.
0:00 The match begins.
Live text and data provided by The Press Association.
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