Billy Clarke and James Hanson turned the game on its head at Valley Parade after Dele Alli had netted the opener for the Dons, who missed the chance to knock Bristol City off top spot.
A poor playing surface - dubbed "one of the worst in the country" by Sunderland boss Gus Poyet as he prepares to make the trip to Yorkshire at the weekend - made for an intriguing contest that burst into life with two goals in three minutes just after the restart.
Bradford goalkeeper Jordan Pickford scuffed an attempted clearance only as far as Jonson Clarke-Harris and he slid a simple pass that Alli finished well to put the visitors ahead after 54 minutes.
But Clarke hauled the sides level when he beat the offside trap to superbly control Gary Liddle's header before slotting home with his other foot.
Hanson then put the home side in front with 20 minutes left, but his seventh league goal of the campaign was controversial.
Jon Stead appeared to handle the ball in the build-up, but play was waved on and his pass sent Hanson clear to steer low past the onrushing David Martin.
Fresh from beating Chelsea 4-2 at Stamford Bridge in the FA Cup in January, Bradford go into the Sunderland clash brimming with confidence of claiming another upset.
