James Hanson had a first-minute chance for the Bantams but he fired over the crossbar and, after that, it was all Stanley.
The promotion-chasing Reds opened the scoring in the ninth minute thanks to a wonder goal from midfielder Luke Joyce. He controlled the ball on the edge of the area, got the better of defender Jon Worthington and curled his effort into the top corner of the net for his first goal in over a year.
Andy Procter doubled the advantage on 16 minutes when Terry Gornell passed to the captain on the edge of the box, and he unleashed a fierce shot to beat keeper Lenny Pidgeley. Stanley came close to a third when Sean McConville set up the in-rushing Ian Craney on the edge of the area but he fired inches wide.
The third goal came on the stroke of half-time when a Jimmy Ryan throw was flicked on at the near post by the Bantams defence, and it was an easy finish for McConville to tap in at the far post for his 13th league goal of the season.
Stanley face Shrewsbury on Monday and victory at the New Meadow will mean the Reds will challenge for automatic promotion while Bradford are left battling against the drop.