David Syers scored late on for Bradford, who beat Aldershot to all but end their relegation worries.
Omar Daley curled a shot into the top corner to put the Bantams ahead, before James Hanson hit the post.
Alex Rodman also struck the upright for the Shots, who went on to equalise when Peter Vincenti fired in a low shot.
Syers headed in a Gareth Evans corner to win it for the Bantams late on and put them six points clear of the drop zone with two games left.
Bradford City interim manager Peter Jackson told BBC Radio Leeds:
"It was a good game today but we needed a performance after what went on at Accrington which was simply not acceptable. They needed a performance today for the fans and they really did that and we could have won by more.
"We created chances, we looked strong but the most important thing was to win the game today and we did it.
"Full credit to the players, they've bounced back with a strong and committed performance."