City's hopes of a fourth straight win were wrecked by a stoppage-time equaliser.
David Poole struck in the first of five added minutes to earn Stockport a deserved point.
But it was still a cruel blow for the Bantams who, for the second home game in a row, had played a large part with only ten men.
Paul Heckingbottom was harshly sent off eight minutes into the second half as the game burst into life after a forgettable opening period.
Donovan Ricketts, back just in time from Jamaica, pulled off two good saves. But he also spilled a corner at the feet of Matty McNeil, who was denied on the line by Peter Thorne's block.
Matt Clarke nearly scored for City but they took the lead with 19 minutes left. Paul Evans picked out Guylain Ndumbu-Nsungu and he smashed his sixth goal for the club with an unstoppable shot into the bottom left corner.
That looked to have sealed City's fourth win in a row but Stockport pressed late on and Poole struck at the death.
CITY: Ricketts, Williams, Wetherall, Clarke, Heckingbottom, Phelan, Evans, Nix, Law, Ndumbu-Nsungu, Thorne. Subs: Daley, Ainge, Conlon, Bentham, Waite.
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