Will Hatfield's last-minute goal won Accrington a point and left Bradford without a home victory in 2012.
Nahki Wells put the Bantams in front when he collected Lee Bullock's long pass before cutting in and scoring with an effort that went in off the bar.
But substitute Hatfield, who had only been on the pitch for five minutes, levelled with a shot at the far post following Kevin McIntyre's corner.
The result means Bradford have drawn each of their last five home games.
VIEWS FROM THE DRESSING ROOM
Bradford assistant manager Steve Parkin told BBC Radio Leeds:
"I think the first half it was very even.
"Yet again we're bitterly disappointed in the goal we conceded today like we did.
"The linesman made the decision to give the corner then he's given the goal quick enough, so we were really disappointed with the decisions."