The Blues skipped away to an early lead when Kenedy opened his Premier League account with the fastest goal in the competition this season.
The Brazilian, in just his second league start, was allowed to run at the Canaries defence after receiving a pass from Eden Hazard wide on the left before advancing inside and firing between the legs of Ryan Bennett and in past John Ruddy to open the scoring just 39 seconds after kick-off.
Chelsea went into the break 2-0 up in controversial circumstances when Diego Costa poked past Ruddy on the strike of half-time but replays showed he was offside when Bertand Traore clipped into his path.
Nevertheless, the goal stood and Guus Hiddink's men were in control at the break as Costa notched his eighth goal in his past 10 league outings.
Redmond had a chance to tie it up later on but was snuffed out by Courtois as Norwich fell into the drop zone despite a gusty effort against the in-form Blues who move up to eight on the back of a 12-game unbeaten run.
2015/16 Barclays Premier League - season scores