The Mariners found themselves up against it when centre-half Robert Atkinson was red-carded for hauling down City striker Michael Boulding as he tried chase down a long clearance.
The dismissal handed Bradford the initiative, but they found Grimsby keeper Phil Barnes in defiant mood and he pulled off a series of excellent saves to frustrate the home side.
Bradford had already shown their intent with most of the early action in the Grimsby box and they turned up the heat after Atkinson's departure.
Winger Steve Jones saw his close-range shot brilliantly kept out by Barnes' out-stretched left leg and soon after the on-loan flyer had another shot rebound off the inside of a post.
Just before the break Bradford midfielder Nicky Law surged into the Grimsby box, but again Barnes stood up well and blocked his fierce drive with his legs.
Bradford keeper Rhys Evans was finally called into action when he saved Stuart Elliott's shot, but it was one-way traffic as Grimsby tried to hold out against superior numbers.
Barnes did well to tip another effort from Law round the post just after the hour, but he was finally beaten when the impressive midfielder latched onto a neat pass and drilled a low shot beyond the Mariners keeper with only 15 minutes to go.
Town midfielder Dean Sinclair almost grabbed an unlikely equaliser when his looping overhead kick drifted over the City bar with two minutes left, but the Bantams wrapped up the win in injury time when they caught Grimsby on the counter-attack.
Substitute Joe Colbeck showed a cool head to set Jones clear and, with only Barnes to beat, he slid the ball home from ten yards to notch his first goal since joining the Bantams on loan.
It was a much-needed victory for Stuart McCall's men and they could consolidate their position in the promotion frame when they entertain rivals Darlington in front of the television cameras on Monday night.