The match was decided in empathic fashion from a free-kick midway through the first half.
Midfielder Jake Sedgemore was brought down 25 yards out, got up, dusted himself down and then cracked a lovely effort beyond the despairing dive of Grimsby's keeper Anthony Williams.
Shrewsbury were much the better side in the first half and could have been two or three goals up by the break, with a particularly glaring miss from defender David Walton who headed over a gaping goal following a corner.
Grimsby came out for the second half in much more determined fashion and twice hit the woodwork, first through striker Martin Gritton, and then through midfielder Thomas Pinault in the fourth minute of stoppage time.
At the other end Shrewsbury were also denied by the woodwork when it appeared that Williams had touched the ball over the top.
And although Shrewsbury had to dig deep defensively in the second half the shout from the home crowd of, "what a load of rubbish" showed what they thought of Grimsby's efforts.
So Shrewsbury are gradually hitting form at the right time following their 4-1 home win over Leyton Orient with four points on their travels from two games.
For Grimsby it is all going wrong and this latest defeat, following losses against Northampton and Lincoln, leaves them marooned below midway with no chance of making the play-offs.
Manager Russell Slade has clearly lost the backing of the supporters and, after two successive relegations, this season is fast disappearing into another really disappointing one for the Mariners.