Nahki Wells fired the Bantams ahead but Jonson Clarke-Harris levelled for a Latics side who are unbeaten in seven home games.
Bradford almost led on the quarter-hour mark when Wells hit a post from close range before the follow-up from Gary Jones was superbly saved by Oldham goalkeeper Mark Oxley.
The breakthrough came after 21 minutes as winger Garry Thompson crossed to Wells, who rifled home from six yards for his 14th goal of the season.
Oldham hit back just two minutes later, though, with James Wesolowski teeing up Clarke-Harris for an unstoppable 15-yard drive into the roof of the net.
Bradford thought they should have had a penalty after 58 minutes but instead Kyel Reid was booked for diving inside the area.
Oldham went closest to snatching a winner when substitute Michael Petrasso fired over from a difficult angle.