Paul Simpson's men are now unbeaten in seven matches, but six of those games have been draws, although they continue to cling to the final play-off berth.
For their fifth draw on the trot, the home side came from behind to earn a point - Barry Conlon giving Grimsby the lead ten minutes after the break, only for Ben Davies to level for the Shrews three minutes later.
In windy conditions neither side were able to gain the upper hand and despite good chances at both ends this was often a ragged, untidy encounter.
Grimsby however, will take more satisfaction from the outcome, securing a vital point in a bid to preserve their Football League status.
Shrewsbury began brightly enough and with winger Chris Humphrey giving the visitors' defence some anxious moments, it only seemed a matter of time before a goal came.
It should have arrived as early as the eighth minute when Humphrey crossed dangerously into the goalmouth - Mariners keeper Wayne Henderson blocked the initial effort from David Worrall, but when the ball rebounded to Davies he steered over with the goal at his mercy.
On the half-hour mark Humphrey broke clear of the Grimsby rearguard and although he took the ball around Henderson, the chance went begging as the Shrews winger eventually fired over from a wide angle.
As the half closed Mike Newell's side brought some purpose to their attacking play and a low drive from Nick Hegarty was pushed away by Shrews keeper Luke Daniels.
In the 55th minute it was Grimsby who made the breakthrough and when Shrewsbury's defence failed to clear a James Hunt centre, Hegarty returned the ball into the danger area - where Conlon was on hand to score his 13th goal of the season.
Three minutes later however, it was goal number 13 of the campaign for Davies when he levelled with an angled drive after good work from substitute Steve Leslie, who had only been on the field 60 seconds.
As the game drew to a close top scorer Grant Holt was unable to convert from close range as Shrewsbury pressed for a winner.
But late on it required a diving stop from Daniels to deny Conlon as the visitors almost snatched all three points.