Jason Holt put the hosts in front just before the hour but they had to settle for a point following Billy Clarke’s equaliser late in the game.
Bradford made a bright start with Andy Halliday putting a first-time shot narrowly wide and then Clarke slipping a good ball through to James Hanson whose effort was saved by Mark Howard.
Clarke then produced a neat shot on the turn which forced Chris Basham to clear off the line.
Jamie Murphy sliced a shot wide from a good position before United took the lead when Michael Doyle had a shot blocked and the ball fell into the path of Holt, who found the back of the net from close range with 57 minutes on the clock.
After Bradford substitute Mark Yeates had a volley saved and a shot headed clear by John Brayford, Clarke equalised with a shot from the edge of the area with six minutes remaining.
Rory McArdle was sent-off in the 90th minute for the visitors after receiving a second yellow card.