The hosts grabbed the lead midway through the first half. After Junior Brown's effort was tipped around the post by City goalkeeper Matt Duke, Alan Goodall headed home at the near post from the resulting corner.
But the Capital One Cup finalists turned the game on its head with goals either side of half-time.
Nathan Pond brought down Bradford skipper Gary Jones 25 yards out and Nahki Wells' free-kick floated beautifully over the wall and past Scott Davies in the Fleetwood goal.
Shortly after the break the visitors took the lead. Will Atkinson's long ball eluded Brown and Shaun Beeley and substitute Ryan Dickson capitalised to shoot low past Davies.
The home side were handed a way back into the game with 15 minutes remaining when James Hanson handled the ball in the box. Jon Parkin blasted home from the penalty spot.
Both sides had chances to snatch victory in five minutes of added time. Ryan Crowther blasted over for the home side before Kyel Reid launched a cross from the left, but nobody was in the box trying to get that vital touch.