Juan Mata's superb strike moved Chelsea to within four points of second-placed Manchester City and consigned Norwich to a second successive defeat.
Mata lit up a cagey game with a 25-yard shot before the break that just beat Mark Bunn and flew in off the post.
Norwich played with plenty of bite and spirit but did not force Blues keeper Petr Cech into a noteworthy save.
Sebastien Bassong came closest for the hosts with a downward header that bounced over the bar late on.
Apart from that injury-time scare Chelsea were untroubled.
And although they never looked likely to get anywhere near reaching the heights of the stunning 8-0 win over Aston Villa, interim manager Rafael Benitez will have been thrilled with a thoroughly professional display.
Benitez had opted for the more defensive-minded John Mikel Obi ahead of Frank Lampard in midfield and the same fluency and slick passing which had blown away Villa was in short supply.
The first 20 minutes were devoid of quality, chances and indeed incident.
Norwich were comfortable in defence, even though they offered little going forward as they looked to bounce back from the 2-1 defeat by West Brom which had ended their 10-game unbeaten run.
But Victor Moses, Mata and Oscar began to see plenty of the ball in the second half of the first period.
David Luiz's willingness to run forward from midfield began to stretch the home defence and he twice shot wildly wide, while Mikel went close to grabbing his first Premier League goal with a fierce rising drive that went just over.
And the pressure told when Mata smashed home his 13th goal of the season with a breathtaking 20-yard left-foot strike. Oscar wriggled away from a challenge and found the Spaniard, who beat Bunn with a fierce strike that the keeper did well to get his fingertips too.
There was nothing unlucky about Juan Mata's 13th goal of the season. It was a terrific strike and was enough to earn Chelsea all three points. Norwich did not really test Peter Cech in the Chelsea goal and their best chance came in injury time when Sebastien Bassong's header went over the bar.
The visitors almost made it 2-0 just after the interval, but Bunn did well to keep out a lunging effort from Moses following a clever near-post corner routine, while Moses also went close with a low strike following a Cesar Azpilicueta cross.
Chelsea showed no signs of trying to settle for a risky 1-0 scoreline but the Canaries began to commit greater numbers to attack and play with far greater urgency.
The ever-dangerous Wes Hoolahan provided their main threat but still they could not create opportunities.
Fit-again captain Grant Holt dragged a shot wide from an offside position after a fine pass from Hoolahan and a couple of Hoolahan set-pieces could easily have led to goals.
Their best chance came in the dying seconds, when Bassong's downward header from a corner went comfortably over the bar.
Chelsea held on, but they failed to close the 11-point gap on leaders Manchester United, who beat Newcastle with a injury-time strike.
Norwich manager Chris Hughton:
"This is a side that have just put eight past Aston Villa. We are playing against Chelsea who are on the back of a really good run and if you make the game too open they can really hurt you.
"If we had a little bit more quality in the final third we could have got something, but it is difficult to get it right in both areas.
"We were right in it. Our goalkeeper has not had to make too many saves [to make] and the one bit of quality shown by them was from Mata.
"That's why Chelsea pay the money they do for the likes of Mata.
"We have been on a good run. We have lost the last two games by one goal. If the lads keep putting in the shift they have [been doing] we will get our points."
Chelsea interim manager Rafael Benitez:
"We knew that was a difficult pitch. They won against Manchester United and Arsenal. It was tough and the weather was not helping.
"I was really happy with the performance of the players. The team are showing character. I am really pleased with the work-rate and the style of play.
"They didn't have too many chances and we had two or three to score a second goal.
"With these kind of games against teams who are strong physically, you have to be careful.
"Juan is a player who can make the difference - we are really pleased with him. He is playing really well.
"Even without the ball he is working hard but when we are in possession he is making the difference. I always say the same, if the team are playing well these players can make the difference."
Live Text Commentary
Full Time The final whistle goes and the game is over.90:00 +1:29
Inswinging corner taken from the right by-line by Robert Snodgrass, Sebastien Bassong has a headed effort from close range and clears the crossbar.90:00 +0:31
Robert Snodgrass sends in a cross, Ashley Cole makes a clearance.90:00 +0:31 Substitution
Substitution Nathan Ake comes on in place of Juan Mata.90:00 +0:31 Booking
Booking The referee shows Eden Hazard a yellow card for unsporting behaviour.90:00 +0:22
Eden Hazard challenges Russell Martin unfairly and gives away a free kick.90:00 +0:03
Unfair challenge on Robert Snodgrass by Fernando Torres results in a free kick. Javier Garrido takes the direct free kick.87:58 Substitution
Substitution Elliott Bennett is brought on as a substitute for Wesley Hoolahan.87:27
Eden Hazard takes a shot. Save made by Mark Bunn.86:01
A cross is delivered by Javier Garrido.85:22
Emboaba Oscar challenges Wesley Hoolahan unfairly and gives away a free kick. Mark Bunn takes the direct free kick.84:28
Fernando Torres delivers the ball.82:32
Sebastien Bassong gives away a free kick for an unfair challenge on Eden Hazard. Petr Cech takes the free kick.81:48
Unfair challenge on Jonathan Howson by David Luiz results in a free kick. Javier Garrido delivers the ball from the free kick left-footed from own half, clearance made by Branislav Ivanovic.81:03 Substitution
Substitution Jonathan Howson replaces Bradley Johnson.80:48 Booking
Booking Bradley Johnson receives a yellow card.79:28
Cesar Azpilicueta sends in a cross, Headed effort from deep inside the penalty area by Juan Mata misses to the left of the goal.78:51
Frank Lampard takes a shot. Blocked by Alexander Tettey.77:56 Substitution
Substitution Eden Hazard joins the action as a substitute, replacing Victor Moses.77:56 Substitution
Substitution Steve Morison on for Anthony Pilkington.
Juan Mata fouled by Grant Holt, the ref awards a free kick. David Luiz takes the free kick.74:04
A cross is delivered by Javier Garrido, clearance made by Branislav Ivanovic.73:33
David Luiz challenges Anthony Pilkington unfairly and gives away a free kick. Mark Bunn restarts play with the free kick.73:13
Corner taken by Emboaba Oscar from the left by-line.72:46 Substitution
Substitution Mikel leaves the field to be replaced by Frank Lampard.71:28
Emboaba Oscar produces a cross.69:56
Outswinging corner taken from the left by-line by Robert Snodgrass, Russell Martin gives away a free kick for an unfair challenge on Mikel. Free kick taken by Petr Cech.69:32
Corner taken by Robert Snodgrass from the left by-line, clearance by Gary Cahill.69:25
A cross is delivered by Anthony Pilkington, clearance by Gary Cahill.68:13
Cesar Azpilicueta produces a cross, Victor Moses has an effort at goal from deep inside the area missing to the left of the goal.67:53
A cross is delivered by David Luiz, clearance made by Michael Turner.65:45
A cross is delivered by Juan Mata.65:27
Corner taken by Juan Mata from the left by-line, clearance by Michael Turner.65:04
Corner taken left-footed by Juan Mata from the left by-line, Bradley Johnson makes a clearance.63:25
Effort on goal by David Luiz from long range goes harmlessly over the bar.61:43
Free kick awarded for an unfair challenge on Wesley Hoolahan by David Luiz. The free kick is delivered left-footed by Robert Snodgrass from right channel. The official flags Sebastien Bassong offside. Petr Cech takes the indirect free kick.60:20
Anthony Pilkington produces a drilled right-footed shot from 12 yards. Save made by Petr Cech.57:58
The ball is swung over by Wesley Hoolahan.56:41
The offside flag is raised against Wesley Hoolahan. Free kick taken by Petr Cech.56:11
The ball is crossed by David Luiz.55:49
The ball is crossed by Victor Moses, Sebastien Bassong manages to make a clearance.54:49
Victor Moses fouled by Bradley Johnson, the ref awards a free kick. Strike on goal comes in from Juan Mata from the free kick, save by Mark Bunn.53:56
The referee blows for offside against Grant Holt. Petr Cech restarts play with the free kick.53:38
The ball is delivered by Juan Mata, Sebastien Bassong makes a clearance.53:14
The ball is delivered by Robert Snodgrass, Gary Cahill makes a clearance.52:50
Javier Garrido sends in a cross, clearance by Branislav Ivanovic.51:42
The ball is swung over by Cesar Azpilicueta, Victor Moses has a drilled shot. Save by Mark Bunn.50:09
The ball is sent over by Cesar Azpilicueta, Fernando Torres takes a shot. Blocked by Sebastien Bassong.49:17
Mikel takes a shot. Michael Turner gets a block in. Effort from outside the area by Ashley Cole goes wide right of the goal.48:56
Corner crossed in by Emboaba Oscar.48:16
Inswinging corner taken right-footed by Emboaba Oscar from the left by-line to the near post, Victor Moses takes a shot. Save made by Mark Bunn.46:36
The ball is crossed by Javier Garrido, Branislav Ivanovic makes a clearance.45:01
The referee blows his whistle to start the second half.45:00 +1:03 Half time
Half Time The referee calls an end to the first half.45:00 +0:17
Effort from 20 yards by Robert Snodgrass. Blocked by Branislav Ivanovic.44:42
The referee penalises David Luiz for handball. Indirect free kick taken by Mark Bunn.40:42
Robert Snodgrass takes the inswinging corner, Bradley Johnson has a header from close in and clears the crossbar.40:35
The ball is sent over by Anthony Pilkington, Ashley Cole makes a clearance.39:55
The ball is crossed by David Luiz. Juan Mata is caught offside. Mark Bunn takes the free kick.39:04
Shot from outside the penalty box by Robert Snodgrass goes wide right of the goal.37:54
Assist by Emboaba Oscar.37:54 Goal scored
Goal! - Juan Mata - Norwich 0 - 1 Chelsea A goal is scored by Juan Mata from outside the box to the bottom right corner of the goal. Norwich 0-1 Chelsea.36:29
Shot by Juan Mata from 18 yards. Blocked by Michael Turner.35:59
Emboaba Oscar takes a inswinging corner to the near post, Grant Holt makes a clearance.35:52
Victor Moses produces a cross, clearance by Sebastien Bassong.35:12
The ball is crossed by Ashley Cole, clearance by Javier Garrido.33:49
Shot from just outside the box by Mikel goes over the bar.33:07
The ball is delivered by Juan Mata, Victor Moses takes a shot. Michael Turner gets a block in.30:46
Russell Martin produces a cross, clearance made by David Luiz.29:34
Effort from deep inside the box by Juan Mata hits the post.29:12
A cross is delivered by Cesar Azpilicueta, clearance by Sebastien Bassong.26:04
Anthony Pilkington produces a cross.25:23
Centre by Cesar Azpilicueta, clearance by Sebastien Bassong.24:38
Juan Mata takes a shot. Blocked by Sebastien Bassong.22:53
David Luiz has an effort at goal from just outside the box which goes wide of the right-hand post.22:29
A cross is delivered by Javier Garrido, clearance by Mikel.21:31
Robert Snodgrass fouled by Victor Moses, the ref awards a free kick. Direct free kick taken by Mark Bunn.21:18
Mikel sends in a cross, clearance by Michael Turner.20:53
The ball is crossed by David Luiz, Alexander Tettey manages to make a clearance.20:17
Corner taken left-footed by Juan Mata to the near post, clearance made by Grant Holt.20:06
The ball is crossed by Victor Moses, Russell Martin makes a clearance.19:04
Effort on goal by David Luiz from outside the box goes harmlessly over the bar.17:47
Grant Holt concedes a free kick for a foul on Cesar Azpilicueta. Direct free kick taken by Petr Cech.16:18
Emboaba Oscar fouled by Alexander Tettey, the ref awards a free kick. The free kick is delivered left-footed by Juan Mata from left channel, Javier Garrido makes a clearance.15:41
The ball is sent over by Bradley Johnson, clearance by Branislav Ivanovic. Russell Martin takes a shot. Mikel gets a block in.14:39
Corner from the right by-line taken by Robert Snodgrass, Gary Cahill makes a clearance.13:17
Branislav Ivanovic sends in a cross, comfortable save by Mark Bunn.11:14
Emboaba Oscar fouled by Robert Snodgrass, the ref awards a free kick. The free kick is delivered right-footed by Emboaba Oscar from left channel, clearance by Alexander Tettey. Cesar Azpilicueta takes a shot. Anthony Pilkington gets a block in.9:24
Robert Snodgrass takes a shot. Gary Cahill gets a block in. Shot from just outside the penalty box by Alexander Tettey misses to the left of the target.6:19
The assistant referee flags for offside against Wesley Hoolahan. Free kick taken by Branislav Ivanovic.5:49
A cross is delivered by David Luiz, save made by Mark Bunn.3:44
The ball is sent over by David Luiz.0:00
The match has kicked off.
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