Chris Eagles scored both goals as in-form Burnley won again.
Eagles fired home from Chris McCann's left-wing cross on 55 minutes and tucked away Robbie Blake's cross from the opposite flank five minutes later.
McCann, Wade Elliott and Kevin McDonald went close to scoring a third for the Clarets before Blake had a free-kick well saved by keeper David Marshall.
Norwich were a threat in the first half and Sammy Clingan volleyed wide of the Burnley goal from 18 yards out.
Burnley boss Owen Coyle on Chris Eagles and Robbie Blake:
"I thought they were both outstanding. Robbie's been chomping at the bit and had a point to prove today, which he did. We all know the quality he has
"As for Chris, the quality of his goals was there for all to see. It's taken him time to adjust after coming from arguably the biggest club in the world (Manchester United) but he's forced his way into our team and he's starting to flourish.
"He's not the finished article yet but he's learning all the time."
Norwich boss Glenn Roeder told BBC Radio Norfolk:
"I didn't feel we showed enough courage, and I'm not happy with any team of mine that doesn't show courage.
"Sometime you lose, and if you've done everything you can to win, you have to put your hands in the air and say; 'we did all we could but it wasn't good enough on the day.'
"I don't believe we've done all we could today, I don't think there was enough good performances throughout the team," he said.
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