Diego Costa ended his six-game goalless run with the winner to stop the Chelsea rot.
The Spain striker curled in a 64th-minute finish and raised his arm in relief as his barren run came to an end.
The victory prevented the Champions, 16th at the start of play, from losing four matchers in succession for the first time under Roman Abramovich.
Boss Jose Mourinho also enjoyed only his third clean sheet in Chelsea’s 13 League games this season.
Norwich’s run of not winning an away game since August 15 continued here after chances were blown earlier by Nathan Redmond and Dieumercik Mbokani.
Here are five things Darren Lewis learned at Stamford Bridge:
1) Baba Rahman had better start having a look around
A regular at German club Ausburg last year, the 21-year-old has started just two games in League so far. It is exactly the situation that had him apprehensive about trading the Bundesliga for the Premier League in the summer. He must have been gutted to see rookie forward Kenedy in his position here.
2) Nemanja Matic is looking like the midfielder from last season again
Good decision making, alert in the tackle and an influence in midfield again. The international break appears to have done him some good.
3) The Chelsea fans’ frustration with the players is increasing
On a number of occasions here there the home fans made their feelings clear about the apparent lack of appetite from a couple of Chelsea players.
They groaned a back-heel from Branislav Ivanovic went out of play. They moaned groaned after Hazard’s cut-back went into the six yard box instead of to Costa in space.
And they were at it again in the second half when Hazard’s ball went into the six yard box but nobody showed a willingness to cash in.
4) Diego Costa is still struggling to find his goalscoring feet this season
His radar seems to be all over the place. Last season you would have put your mortgage on his scoring with even the slightest sniff of goal.
Here, his nightmare start to the campaign continued as he skied one from eight yards, he allowed Ruddy to save with his legs just before the break and he simply struggled to convince.
Eventually, he was able to end his gaol drought. but Loic Remy must really have upset someone at Stamford Bridge to not be playing with Costa in this form.
5) Norwich need more cutting edge
They had chances but just couldn’t take them.
And against a side with Chelsea’s confidence they should have done. The efforts on goal that they did have, from Redmond and Mbokani, were either easy for Asmir Begovic or wayward when they should have been on target.
Darren Lewis’ player ratings:
Begovic 8 – Good save from Redmond’s 14th-minute angled drive. Even better from Brady on 68.
Zouma 7 – Should have done better with his effort from Willian’s corner. Unlucky to hit the bar from Willian free-kick.
Ivanovic 6 – Started okay but given a tough time by Brady, Redmond and Mbokani.
Terry 7 – Unlucky with his 13th-minute flick from Willian corner. Great block to deny Bassong.
Kenedy 7 – A surprise starter at left-back – but did a better job than Ivanovic on the other side.
Matic 9 – Getting his mojo back. Slick passing. Good anticipation
Fabregas 7 – Unlucky to see his 10th-minute effort go over the bar from close range.
Hazard 8 – Sharp again. Sent some nice balls into the box. Nobody there to cash in though!
Willian 7 – Quick feet to get his 14th-minute effort away. Lucky not to concede a penalty for his push on Brady.
Pedro 6 – Nice cut-back to tee up Costa on 25 minutes. Industrious throughout.
Costa 7 – His goal will have done him the world of good. Average until then.
Ramires (Willian 87)
Azpilicueta (Hazard 90)
Ruddy 6 – Fine save from Willian’s 14th-minute effort. No chance with the goal.
Wisdom 5 – Did well enough against a combination of Pedro and Kenedy.
Bassong 6 – Went to sleep for the goal. Rightly booked for his pull on Hazard.
Howson 5 – Industrious but unable to repel the threat from the home side. Replaced.
Olsson 5 – Rightly booked for clattering Costa as the striker raced in on goal.
Bennett 5 – Great tackle on Hazard to prevent the Belgian scoring Chelsea’s second.
O’Neil 5 – Rightly booked for his foul on Hazard just after half time.
Mulumbu 6 – Worked hard to try and deny time and space to Chelsea’s creative players.
Brady 6 – Linked up well with Redmond and Mbokani to cause early problems.
Redmond 6 – Worked hard in support of Mbokani up front. But couldn’t provide enough cutting edge.
Mbokani 5 – Should have done better with his 19th-minute shot from inside the box.
Hoolahan (Howson 72) 5
Jerome (Mbokani 72) 5
Mulumbu (Dorrans 72) 5
Man of the Match: Matic
Ref: Craig Pawson