After scoring eight at the weekend against Aston Villa, Juan Mata's brilliant first half strike proved to be enough for Chelsea to boost their title chances.
Norwich struggled to create too many goalscoring opportunities with Sebastien Bassong's header over the top in stoppage time their best chance of the game.
In the early exchanges chances were few and far between with defences very much on top.
David Luiz, who was again playing in midfield, had a few sights of goal but he failed to trouble Mark Bunn in the Norwich goal with a couple of wayward efforts.
Chelsea created the best opening of the game on the half hour mark when Luiz slipped Mata in on goal, but the Spaniard could only hit his shot into the side-netting.
The visitors were beginning to get on top and four minutes later Luiz teeed up John Obi Mikel on the edge of the box only for the Nigerian to drill his powerful shot over the crossbar.
Chelsea broke the deadlock on 38 minutes as Mata netted his 13th goal of the season with a superb shot from the edge of box.
There looked very little on when Mata picked up a pass from Oscar 30 yards from goal, but with very little backlift he fired a fierce shot past Mark Bunn into the corner of the net.
Bunn had to be alert early in the second half to divert Oscar's deflected corner at his near post as Chelsea pushed for a second goal.
Mata tried to catch out Bunn on 55 minutes with a quickly taken free-kick from the edge of the box with the keeper still organising his wall, but he got back to save the curling effort.
Victor Moses really should have added a second goal on 68 minutes when he brought down Cesar Azpilicueta's cross inside the box on his chest, but he drilled his shot wide of the target.
Norwich pushed everything forward in the closing stages in a bid to find an equaliser, but the closest they came was deep into injury time when Bassong headed down into the ground and over the crossbar as Chelsea secured all three points.