Norwich slid deeper into relegation trouble after handing Burnley victory inside the opening four minutes.
The Canaries' resistance lasted just 51 seconds as an exhilarating Burnley attack culminated in Robbie Blake heading home Wade Elliott's cross.
Burnley made it 2-0 three minutes later when Jon Otsemobor hacked down Blake and Andy Gray dispatched the penalty.
Chris Brown sidefooted home on 68 minutes but Norwich still slumped to a sixth defeat in seven games.
Burnley boss Steve Cotterill:
"We made a great start.
"We had plenty of ball in the first half but we didn't build on that in the second-half.
"If we'd got a third then we would have had no problem, but we held on and the lads deserve credit for that."
Norwich caretaker boss Jim Duffy:
"I didn't think it was a penalty. The referee gave a decision that baffles you as a manger and surprised even the Burnley players.
"We came back in the second half but it wasn't quite enough."
Burnley: Kiraly, Alexander, Carlisle, Unsworth, Jordan, Elliott, McCann, Spicer, Lafferty (Akinbiyi 78), Blake (Mahon 57), Gray.
Subs Not Used: Jensen, Harley, James O'Connor.
Booked: Unsworth, Alexander.
Goals: Blake 1, Gray 4 pen.
Norwich: Marshall, Otsemobor, Murray, Shackell, Lappin, Chadwick (Cureton 69), Brown, Russell (Smith 84), Huckerby, Strihavka (Hartson 58), Spillane.
Subs Not Used: Croft, Martin.
Goals: Brown 68.
Ref: Michael Jones (Cheshire).