A tight first half saw the Stags have the edge and they were unlucky to find themselves behind to Bradford’s first real threat on goal after 19 minutes.
Callum Cooke sent over a right-wing corner and Paudie O’Connor was unchallenged to bury a far-post header.
But Mansfield continued to probe and were finally level in the 37th minute when Ollie Clarke crossed from the left byline and Oli Hawkins was there to send a header high into the right of the net.
Mansfield roared ahead after 52 minutes when Stephen Quinn sent Rhys Oates to the left byline and his pull-back was expertly volleyed into the bottom-right corner by Hawkins.
City were level nine minutes later as Cooke attacked the home box and set up Charles Vernam to his left, who tucked home an unstoppable finish across goalkeeper Nathan Bishop.
With four minutes to go Richard O’Donnell did well to keep out a far-post Elliott Hewitt header from Stephen McLaughlin’s cross.
And within a minute Bradford stole it as Bishop saved a low Vernam effort but was helpless as Cook tucked away the loose ball.