The former Manchester United star, who joined the Clarets in the summer, took his tally to four for the season with two sublime second-half finishes.
Owen Coyle's in-form Clarets have now lost just once in their last 15 games in all competitions and on this evidence they look serious contenders for promotion.
Norwich, meanwhile, continue to look nervously over their shoulders after this latest away defeat left them hovering above the Championship's relegation zone.
There was little to choose between the two sides in a breathless first half packed with goalmouth incidents
Darel Russell and Leroy Lita went close for Norwich during a frantic opening five minutes, before Steve Thompson crashed a shot against the post for the Clarets.
The Canaries then had an amazing let-off when Clarke Carlisle had two separate efforts hacked off the line during an incredible goalmouth scramble.
The pendulum then swung firmly in Burnley's favour when they scored twice in four minutes at the beginning of the second half.
Robbie Blake, who was inspirational throughout, slipped a clever ball into Eagles in the 55th minute and the midfielder then strolled purposefully into the box before slotting a cool finish under David Marshall.
The duo then combined again for the second, Blake sending Eagles racing clear and he clipped a cool finish beyond Marshall.
Norwich could have pulled one back late on, but Lita dragged a low shot wide of the far post to complete a miserable afternoon for Glenn Roeder and his players.