A sensational strike from loan signing Moses Ashikodi looked to have given Bradford a vital three points, but a moment of petulant madness from young winger Joe Colbeck changed the course of a tight match
The tense encounter could have gone either way but it was fiery Watford striker Ashikodi who blasted the Bantams into the lead
He was first to Billy Paynter's knock-on and deftly flicked a bouncing ball over the head of defender Sean Gregan.
Then from 20-yards he rifled an unstoppable shot past Les Pogliacomi into the roof of the net.
But for the second home game in succession, City's momentum was halted by a red card.
Steve Schumacher's sending-off against Blackpool may have been harsh, but the referee had little option but to show Colbeck his second yellow card for needlessly kicking the ball away.
Booked in the first period for a dangerous lunge, Colbeck then belted the ball 30 yards down the pitch after running it out of play and was given his marching orders.
The ten-man Bantams battled hard to hold on to their precarious lead and both Luigi Glombard and Miki Roque missed decent openings.
But just as it looked as though the home side might hold out for a precious three points, Glombard spoilt the party.
With just seven minutes on the clock a curling cross was flicked on and the striker was on hand to poke the ball past a desperate Donovan Ricketts.
With a man advantage Oldham then pushed for a winner and were only denied deep into stoppage time when Ricketts produced a superb diving stop to thwart Chris Taylor.
The Bantams did manage to hold on to the point but were so close to winning what had been billed as a must-win game.
A point is of little use to David Wetherall's Bantams, who have now not won at home since December and are staring relegation into League Two for the first time in 25 years squarely in the face.