The Canaries had their relegation confirmed last weekend, but first half red cards for Emiliano Buendia and Josip Drmic made it a painful afternoon for the hosts.
Neither side created much in poor first half hour, before Buendia saw red on 35 minutes.
The Argentinian tangled with Ashley Westwood, and after a quick VAR check, referee Kevin Friend sent him off for an elbow.
However, the hosts were not to be rescued by the half time whistle as Drmic reduced them to nine men after a lunge at Erik Pieters and Chris Wood volleyed Burnley in front.
With Norwich out of the game after the break, Burnley pushed for a second goal, as Tim Krul denied Pieters and Jay Rodriguez.
But despite Krul’s best efforts, this was to be a disastrous final home game for Norwich as Ben Godfrey turned into his own net to secure all three points for Burnley.
FULL TIME AT CARROW ROAD IT’S NORWICH CITY 0 BURNLEY 2