The first half was frankly awful with the match devoid of incident until Grimsby struck on 38 minutes with the opening goal.
The move was totally against anything that had gone before and when Martin Paterson exchanged passes with Nick Heggarty he scored with a cross shot to put the Mariners ahead.
Whatever the Shrewsbury manager Gary Peters said to his team at half time they came out like a different side.
They took the game by the scruff of the neck with the tricky Derek Asamoah a real handful down the right.
The nippy little striker tried his luck from 30 yards only to see his effort beat the keeper, hit the inside of the post, roll along the goal line and out for a goal kick.
But Shrewsbury and Asamoah were not to be denied, and on 52 minutes he set up striker Michael Symes for the equaliser and his 10th goal of the season.
At that stage there looked only one winner and that was the visitors. However, Alan Buckley made two astute substitutions which changed the game.
He withdrew his two wide men although not at the same time replacing Heggarty with Gary Harkins and Peter Till with Isaiah Rankin.
This also saw striker Paterson move out to the left from where he struck the winner on 73 minutes.
He tried his luck from well out on the left and the ball came through a crowded penalty area before nestling in the back of the net.
This goal restored Grimsby's lead but knocked the stuffing out of the Shrews. Although there were four minutes added on they were unable to claw a goal back for the second time.
For Grimsby they did not reproduce the flowing football of the last home game against Accrington but against an inconsistent Shrewsbury side, who on their day can match anything in this division, it was a great result which showed their battling qualities.