Scott Parker’s men looked to be cruising to a thoroughly deserved victory following a dominant first-half display, which saw them lead thanks to goals from Hannibal and Jaidon Anthony.
Norwich set up a nervy final 15 minutes, however, after Jack Stacey bundled home from close range.
But the Clarets held firm and saw out the late pressure to cling on for a 2-1 win, that sees them move five points clear of Sheffield United in third place ahead of the Saturday games.
Here’s how Burnley’s players rated:
13. SUB: Josh Laurent - 6/10
For Hannibal, 77 Unfortunate to be dropped but Burnley needed to freshen things up with some more intensity after a busy week. Photo: Alex Livesey
14. SUB: Jeremy Sarmiento - 6/10
For Edwards, 77 Embarked on a couple of direct runs, but had to head for the corner when he broke through in the dying seconds. Photo: Kelvin Lister-Stuttard
15. SUB: Ashley Barnes - 6/10
For Flemming, 90 Put himself about and offered a physical presence coming up against the side he left in January. Photo: Alex Livesey
16. SUB: Joe Worrall - 6/10
For Anthony, 90 Brought some added height and physicality to Burnley’s backline for the final few moments as Norwich threw men forward. Photo: Matt McNulty