The Black Cats stormed into a deserved 35th minute lead with a stunning goal from Julio Arca, only to be pegged back two minutes later through Graham Branch. But Mick McCarthy's side took the points after a scrambled effort early in the second half from Michael Bridges restored their advantage.
The Burnley goal had survived a couple of near misses before the Black Cats went ahead with a tremendously worked and executed goal, worthy of winning many a match.
Bridges went wide of goalkeeper Brian Jensen only for his shot to be deflected behind for a corner from which Stephen Wright had a block-buster beaten out by Jensen.
The home side was not to be denied however, and deservedly went ahead in the 35th minute. Bridges jinked his way through the middle to release Arca with a delightful pass and the Argentinian fired across Jensen and into the net for his third goal of the season.
Burnley responded within an immediate equaliser. Gary Breen's misplaced clearance gave James O'Connor the chance to set up Branch who made no mistake from close range.
Only a brilliant finger-tip save by Jensen prevented Liam Lawrence from restoring Sunderland's lead on the stroke of half-time and immediately on the resumption Dean Whitehead had a firm header blocked.
The match-winning goal was a scrambled effort following a well-worked corner between Lawrence and Arca. The former's cross-cum-shot was flicked over the line by Bridges, much to the disgust of Burnley boss Steve Cotterill.
Jensen saved well from Chris Brown and after strong appeals for a penalty from a Carl Robinson header had been turned down, Burnley sensed all was not lost.
The much-wanted Robbie Blake had a free-kick charged down and Branch missed a glorious chance of a second equaliser as the visitors pushed forward in the closing stages.