The visitors had made a bright start to the game, with defender Charlie Daniels hitting the crossbar from 25 yards out, but the Londoners were up against it from the moment JJ Melligan was sent off for a studs-up challenge on Adam Drury seven minutes after the break.
The Canaries took time to make their numerical advantage tell, but once substitute Chris Martin latched onto Korey Smith's precise pass to lash the ball home after 75 minutes there was no stopping them.
Paul Lambert's side doubled their advantage when Grant Holt brought down Drury's cross on the left and volleyed home in spectacular fashion.
And the points were secured after 81 minutes when defender Michael Spillane burst into the area from the right before unleashing an unstoppable shot past goalkeeper Jamie James to register his first goal in Norwich colours.
The icing on the cake for the Canaries came deep into injury time when substitute Jamie Cureton rushed clear to slide home his first goal of the season and complete a marginal victory that, while deserved, was a little flattering on the hosts.