Although it was a match Grimsby desperately needed to win they would probably have settled for a point after playing 45 minutes with only ten men.
The dismissal of striker Steve Livingstone for raising his elbow to Bradford skipper Robert Molenaar meant they had a one nil lead to defend with over half the match left.
Although Bradford equalised on 56 minutes with a well struck shot from Andy Gray the sides were still level as the game moved in to three minutes of added time.
Then Claus Jorgensen stuck a superb match winner for his fourth goal in as many games to break the Marinersâ€™ hearts.
Groves said: "We managed to frustrate them in the second half for a lot of the time, but the sending off was a turning point. Its very disheartening to lose so late when there is little in the game."In contrast City boss Nicky Law said "We were disappointed to go one nil down and it was a poor goal to give away.
â€œBut we never panicked and played some good football. We scored 2 very good goals - it was a great finish for the first one and the second was worthy of winning any game."City dominated a scrappy first half they trailed form the15th minute when Terry Cooke sent striker Michael Boulding clean through the middle and he beat former Mariners keeper Aidan Davison to put Grimsby ahead.
The sending off of Livingstone handed City a numerical advantage, although they went down to ten men themselves when midfielder Simon Francis was shown a second yellow card shortly after Cityâ€™s second goal.