The Blues controlled the game for long periods but City made a game of it in the second half and threatened an upset when Leon McKenzie beat Petr Cech with a textbook header to make it all square with 26 minutes left to play.
However, Jose Mourinho made a double substitution which brought an immediate result, with substitute Eidur Gudjohnsen opening up the City defence for the other replacement Mateja Kezman to restore the Chelsea lead.
The result left Norwich deep in relegation trouble but there are positives for Nigel Worthington to draw from this game.
The Canaries kicked off and in the opening two minutes McKenzie forced a corner while at the other end Damien Duff blasted a shot high into the River End stand.
Frank Lampard also fired over before Dean Ashton's shot took a deflection which went un-noticed by the referee.
Young Jason Shackell's header kept out Duff's goal bound shot to give Chelsea the first of three corners inside the first ten minutes. Lampard came much closer with a chipped shot that just cleared the bar.
Joe Cole then opened the scoring after 22 minutes. He battled his way into the City penalty area, shrugging off two tackles in the process, before unleashing a rising left-foot drive which beat Robert Green high to his right.
Ashton then had one shot deflected for a corner and another which went too high.
A deflected shot from Lampard went safely into the hands of Green but the City keeper had more to do when he beat Cole to Lampard's diagonal cross, thereby ensuring that the Canaries were only trailing by one goal at half-time.
Claude Makelele required treatment five minutes into the second half after falling heavily, before Didier Drogba headed wide when he got on the end of Lampard's free-kick.
Green beat away a fierce shot from Drogba after he had been put clear by Cole while at the other end Ashton's glancing header from Huckerby's left wing corner drifted wide of the far post.
McKenzie then gave the Carrow Road faithful cause for celebration when he played the ball wide to Huckerby on the left wing before beating Cech with a far post header from the resulting cross.
It was at this point that the Chelsea manager made his double substitution, but before they came into the action Cech had to make an acrobatic save to catch a header from Damien Francis when he got on the end of Graham Stuart's right wing cross.
Gudjohnsen then lifted the ball over the Norwich defence, Lampard helped it on allowing Kezman to score with the outside of his right boot from close range, giving Green no chance.
The Norwich defence seemed to switch off in the 79th minute allowing Ricardo Carvalho a free header at the far post from Lampard's left wing corner to seal victory for the visitors.
McKenzie got a well-deserved round of applause from the home fans for his goal and all round contribution when he limped off in the 90th minute to be replaced by Ian Henderson, but his efforts counted for little at the foot of the table.
MAN OF THE MATCH - Joe Cole
Joe Cole pipped Claude Makelele and John Terry to top spot. His determined run and thundering shot put Chelsea on their way and thereafter he was a constant threat to the Norwich defence with his running and passing.