With Grimsby hanging onto a 1-0 lead they survived a disallowed goal and the sending off of keeper Phil Barnes for handling outside the area before Bradford snatched a dramatic equaliser from the penalty spot in the fourth minute of added time.
Grimsby skipper Justin Whittle brought down sub Luke Medley and Guylain Ndumbu-Nsungu beat substitute keeper Gary Montgomery from the spot.
There was not even time to restart the game before the final whistle blew.
After a poor first half in which neither side threatened a great deal, the only incident of note was when Bradford keeper Rhys Evans had to go off after finally giving in to a hand injury.
Central defender Mark Bower went in goal but was only seriously tested when he saved a Tom Newey free-kick in the second half.
But the replacement keeper had to share some of the blame for a defensive mix-up when he was caught out of his goal and on-loan full-back Shaleum Logan chipped in neatly under the bar on 48 minutes.
After this Grimsby should have pushed on and made certain of the points but they had to rely on keeper Barnes who made some splendid saves to keep Town's lead intact.
It looked as if Grimsby's defensive wall had finally been breached four minutes from time but the referee ruled out the score.
But this was only the start of the late drama which ended with a mini-pitch invasion from the delighted Bradford fans with City manager Stuart McCall taking great credit for going over to them and calming things down.
So this result means that two struggling sides stretched their winless runs, with Bradford having taken two points after five successive defeats and Grimsby picking up their first point in five games.