The visitors were trailing 1-0 when Bradford substitute defender Rob Kiernan, under no pressure, headed the ball past his own keeper Lenny Pidgeley to level the scores after 61 minutes.
Three minutes later Barnet went in front when defender Anwar Uddin scored with a far post header from Glen Southam's corner.
Barnet then scored a third goal after 67 minutes when striker Izale McLeod broke away down the middle before slipping the ball into the path of the unmarked Ricky Holmes to tap the ball into the net.
Bradford had led with a goal in first-half stoppage time from defender Luke Oliver who headed the ball into the net from close range from David Syers' cross.
Fellow defender Shane Duff almost increased their lead two minutes after half-time when he hit the post from close range before going off injured two minutes later.