However, the major talking point was the sending-off of Stefan Payne for head-butting team-mate and former Bradford winger Filipe Morais at the end of the first half.
Morais’s misplaced pass as the game moved into stoppage time resulted in him being head-butted and Sheffield referee James Bell showed the red card.
Grimsby manager Paul Hurst said: “It is something I can’t defend. The pair of them have let down the club, their team-mates and the fans.
“As far as the game was concerned, it made it more difficult than it needed to be. It was more than a little spat. I have to decide what to do for the good of the team.”
The result which ended Grimsby’s eight-match unbeaten run leaves them seven points adrift of safety with eight games left.
The scrappy game was settled in the 42nd minute when Anthony O’Connor scored with a close-range effort from Gareth Evans’s cross after a strong spell of pressure.
Bradford joint-manager Mark Trueman said: “It was a hard earned win. Grimsby are fighting for their lives and their player who was sent off didn’t keep his emotions in check, but I had to keep our players focussed, see out the game and win it.
“As regards the play-offs, it’s all to play for.”
Bradford City: O’Donnell, Cousin-Dawson, P O’Connor, Canavan, Wood, A O’Connor, Watt (Scales 86), Clarke (Vernam 69), Donaldson (Crankshaw 77), Cook (Rowe 69), Evans. Unused substitutes: Hornby, Stevens, Scales.
Grimsby Town: McKeown, Hendrie, Hewitt, Menayese, Hebergham (Waterfall 45), Matete (Lamy 90), Coke (Spokes 83), Williams (Clifton 45), Morais (John-Lewis 45), Hanson, Payne. Unused substitutes: Battersby, Green
Referee: J Bell (Sheffield).
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