Carlos Edwards scored a sensational winner in the 80th minute to the delight of a crowd of 44,448, the highest in the Championship this season, after winning the third penalty kick of the game to set up the equaliser.
It was action all the way with Sunderland's early onslaught eventually rewarded with an eighth goal of the season in the 14th minute for Daryl Murphy. David Connolly crossed from the left and the striker wasted no time in sweeping the ball home from close range.
Connolly, Anthony Stokes and Edwards had all missed chances to break the deadlock and ease the tension of the bumper crowd and a rout looked possible.
But the Black Cats squandered the best chance of all to go further ahead when awarded a 21st minute penalty. Wayne Thomas was adjudged to have brought down Connolly, but justice was done when goalkeeper Brian Jensen turned the Irishman's international's weak spot-kick around the post.
Liam Miller then missed a golden chance to put Sunderland further ahead as he failed to hit the target and the miss proved costly when Burnley drew level in the 38th minute.
Goalkeeper Darren Ward rushed from his line to dive at the feet Wade Elliott, but despite the appeals of the home side, referee Trevor Kettle again pointed to the penalty spot.
Andy Gray gratefully accepted the opportunity to grab his 14th goal of the season against his former club and leave Sunderland with it all to do.
The Clarets, gaining in confidence, swept into a 50th minute lead with a stunning strike from Elliott, but four minutes later Steve Caldwell upended Edwards and Connolly made no mistake with his second spot-kick.
Ten minutes from time, Edwards latched on to a through ball from Murphy and his thundering 25-yard drive left Jensen helpless with a goal worthy of sending Sunderland back to the top of the Championship.