Match ends, Norwich City 1, Chelsea 3.
Late goals from substitutes Eden Hazard and Willian defeated Norwich and gave Chelsea their first Premier League away win of the season.
Oscar put the visitors ahead with a first-time shot from inside the area, but Anthony Pilkington equalised with a header midway through the second half.
Norwich pressed late on but they were punished when Hazard stabbed in after a swift counter attack.
Willian curled in a third a minute later to seal victory.
The win was much needed for Jose Mourinho, with his side having struggled away from Stamford Bridge prior to arriving at Carrow Road.
The Blues boast a 100% record at home in the league but had drawn two and lost one of their first three away games.
But victory at Norwich means they head into the international break third in the table, just two points behind Arsenal and Liverpool.
Norwich, meanwhile, drop into the bottom three after West Ham's surprise 3-0 win at Tottenham.
Denied the services of suspended and injured striker Fernando Torres, Mourinho gave Demba Ba only a second start of the season.
The former Newcastle man was evidently determined to prove his worth, making a nuisance of himself from the outset and taking only four minutes to make a telling impact.
Frank Lampard lofted a pass towards the Norwich area for Ba, who shook off the attention of a defender to bring the ball under control and then clip a pass for the onrushing Oscar, who finished with the outside of his boot.
It was all so effortless, a word that summed up Chelsea's play in the early stages of the game as they sprayed passes around with ease.
Only a smart save from John Ruddy prevented the visitors adding a second in the 14th minute as Juan Mata showed great vision to cut open the Norwich defence and put Ba clear on the left, but his low shot was tipped wide by the City goalkeeper.
Still, the visitors needed to be alert at the back as Norwich's first chance almost brought the equaliser. Robert Snodgrass got in behind the Chelsea defence and crossed for Jonny Howson, but his close-range shot was kept out by Petr Cech at his near post.
That chance gave the Canaries belief that openings were there to be exploited and the momentum of the game shifted in their favour after the break.
Winger Pilkington had a penalty appeal waved away after going down in the area under a challenge by Ramires, before John Terry hooked a clearance off the chest of Ricky van Wolfswinkel as the striker attempted to get on the end of Robert Snodgrass's ball.
But the hosts were deservedly level when Van Wolfswinkel cushioned a header from Martin Olsson's cross into the path of Pilkington, who nodded in from barely six yards.
From then on the game was wide open. Chelsea defender Branislav Ivanovic forced Ruddy into a low dive, while the introduction of Nathan Redmond added bite to the Norwich attack and he saw a decent drive saved by Cech.
The home side could sense a possible winner and they pushed forward inside the final 10 minutes, but that ultimately proved their undoing.
Willian sparked a quick counter and fed a pass to Oscar, who in turn picked out Hazard's run and the Belgian capitalised on Alex Tetty's attempted clearance to poke the ball under the body of Ruddy.
A minute later the win was confirmed as Willian pounced on a loose ball before expertly curling a shot into the net for his first Chelsea goal.
Norwich manager Chris Hughton:
"There are lots of positives to take from the game. It [losing] is obviously very difficult to take at this moment. We had worked ourselves back into the game after a difficult start to put ourselves in a position where, when we equalised, I did not think we would lose the game.
"I doubt there was anybody watching who did not feel we did not deserve anything from the game."
- 7SnodgrassSubstituted forRedmondat 81'minutes
- 27TetteyBooked at 69mins
- 9van WolfswinkelSubstituted forHooperat 73'minutes
- 4David Luiz
- 3ColeSubstituted forE Hazardat 75'minutes
- 7Santos do Nascimento
- 10MataSubstituted forWillianat 81'minutes
- 11OscarBooked at 62mins
- 19BaSubstituted forEto'oat 73'minutes
- 17E Hazard
- Neil Swarbrick
- Shots on Target
Second Half ends, Norwich City 1, Chelsea 3.
Offside, Chelsea. David Luiz tries a through ball, but Samuel Eto'o is caught offside.
Corner, Chelsea. Conceded by John Ruddy.
Attempt saved. Frank Lampard (Chelsea) right footed shot from outside the box is saved in the bottom left corner.
Ramires (Chelsea) wins a free kick in the attacking half.
Foul by Sébastien Bassong (Norwich City).
Goal! Norwich City 1, Chelsea 3. Willian (Chelsea) left footed shot from the right side of the box to the top left corner.
Goal! Norwich City 1, Chelsea 2. Eden Hazard (Chelsea) right footed shot from the centre of the box to the centre of the goal.
Corner, Norwich City. Conceded by John Terry.
Attempt blocked. Willian (Chelsea) right footed shot from outside the box is blocked.
Attempt saved. Nathan Redmond (Norwich City) right footed shot from the right side of the box is saved in the centre of the goal. Assisted by Leroy Fer.
Substitution, Chelsea. Willian replaces Juan Mata.
Substitution, Norwich City. Nathan Redmond replaces Robert Snodgrass.
Attempt missed. Robert Snodgrass (Norwich City) right footed shot from outside the box misses to the right. Assisted by Anthony Pilkington.
Attempt missed. Eden Hazard (Chelsea) left footed shot from the centre of the box misses to the right. Assisted by Branislav Ivanovic with a cross.
Attempt blocked. Samuel Eto'o (Chelsea) right footed shot from the left side of the box is blocked.
Attempt saved. Branislav Ivanovic (Chelsea) right footed shot from outside the box is saved in the bottom left corner. Assisted by Andre Schürrle.
Branislav Ivanovic (Chelsea) wins a free kick in the defensive half.
Foul by Anthony Pilkington (Norwich City).