Neil Warnock's promotion favourites produced two goals in a lightning two-minute spell to keep alive their hopes of automatic promotion to the Premiership.
But with an hour gone it looked increasingly unlikely that United would break down a struggling Bradford side until the game turned dramatically with goal from Chris Morgan and Jack Lester in the space of two minutes.
Lester had found a way through in the 13th minute only to be pulled back by centre-back Peter Atherton. The former Sheffield Wednesday defender picked up a booking and Michael Tonge squandered the opportunity, drilling his free-kick high over the top.
Bradford, enjoying a mini revival and undefeated in three games, carved out a chance minutes later. The United back four failed to clear Lewis Emanuel's corner from the right and striker Michael Branch got a touch, but steered his header wide of the target.
United almost found a way through in the 25th minute as Dries Boussatta chased a long ball down the right flank. The former Ajax midfielder beat keeper Clint Davies in a chase for the ball, stabbing it round the advancing keeper as Atherton stuck out a foot to clear off the line.
A sweeping move across field sliced through Bradford on 36 minutes, former Bantams midfielder Stuart McCall finding Tonge who cut cleverly inside and finished with a stinging drive straight at Davies..
Bradford, always dangerous on the break, went close with a Paul Heckingbottom free-kick and Paul Evans almost broke the deadlock cutting out a loose clearance to lash in a low drive, the ball skidding a fraction wide of the near post with Paddy Kenny stranded.
The breakthrough came in the 60th minute, Tonge exchanged passes with McCall from a corner before floating the ball towards centre-back Morgan who finished with a crisp header.
Lester added the second taking advantage of a Mark Bower blunder as he surged into the area to stroke the ball past the advancing Davies from 15 yards.