It would have been three points for the Bantams had they held on a little longer to a lead they had grabbed against the run of play.
Bantams chief Peter Taylor reflected: "We've made mistakes this season and conceded goals and when you concede goals it gets the boys deflated. That's what's happened to us too many times."
Under pressure for almost an hour from a confident County side, the Bantams scored with their first attack of the second half. On 56 minutes, Jake Speight showed plenty of determination to get to the line and put in a cross which David Syers smashed into the roof of the net.
Underlying City's performance was an outstanding display in central defence from Luke Oliver and Shane Duff, who restricted County to speculative long-range efforts.
It seemed that Taylor's men would leave with three points, until one lapse in concentration allowed the Hatters back. On 78 minutes, they were awarded a corner, and with City still arguing over its legitimacy, it was quickly taken and Adam Griffin produced a pinpoint cross for the hosts' leading-scorer George Donnelly, unmarked at the far post, to nod the ball in the back of net.
Despite this setback, the Bantams pressed hard for a winner in the final 10 minutes, with Luke O'Brien and Tommy Doherty both having half- chances.
Stockport County: Glennon, Lynch (Simpson 83), Turnbull, Swailes, Assoumani, Vincent (Fisher 63), Tansey, Conlon (Proctor 63), Donnelly, Griffin, Mainwaring. Unused substitutes: fon Williams, Poole, Pilkington, Halls.
Bradford City: McLaughlin, O'Brien, Oliver, Doherty, Evans (Moult 63), Speight, Hunt, Duff, Bullock, Syers, Threlfall (Osborne 90). Unused substitutes: Daley, Williams, Sexton, Chilika, Horne.
Referee: N Swarbrick (Lancs).
Man of the match: Luke Oliver.
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