Not since March, when they beat Barnet 4-1, had the Mariners triumphed at Blundell Park.
But this was a well-deserved win as, apart from a spell just before half-time, Grimsby were in control as they played some speedy attacking and skilful football.
The home side were quick out of the blocks and looked likely to score at any time. But it took a fine save from keeper Matt Gilks to deny midfielder Liam Trotter.
But the goal would not come and, with leading scorer Grant Holt starting to exert his influence, the visitors began to show why there were second in the table.
But Grimsby were happy to reach the interval on level terms and, no doubt inspired by manager Mike Newell's words, they came out strongly for the second period.
Ivory Coast debut boy Jean-Louis Akpa-Akpro let fly with an effort which went just wide and he played a full part in the game's only goal.
His good run ended with a shot which fell kindly for Adam Proudlock who swivelled and hit the ball home fiercely into the roof of the net.
That 53rd-minute goal proved decisive although Grimsby certainly did not sit on their lead.
Full-back Robbie Stockdale pulled the trigger from 30 yards and Gilks did well to beat the ball away. Then Akpa-Akpro showed a touch of greed when he shot into the side-netting with colleagues unmarked in the middle.
Shrewsbury's only really clear-cut chance came just after the goal when striker Jamie White broke clear but dragged a poor effort wide.