The Shrews chalked up their third win in four matches as second-half goals from Dave Hibbert and Michael Symes enabled them to secure the points, despite the visitors replying with a Ciaran Toner penalty with just over 20 minutes left.
While the previously unbeaten Mariners had the better of the first half exchanges, Shrewsbury took a firm grip of proceedings in the second half and just about deserved to win an often very entertaining, open contest.
The woodwork denied both sides within 60 seconds as the first half began to warm-up nicely.
In the 12th minute Peter Till rifled a shot against the Shrewsbury crossbar, while a minute later Grimsby had an upright to thank as David hunt fired against the foot of the post with visiting goalkeeper Phil Barnes well beaten.
While Grimsby had a greater share of possession in the opening 45 minutes chances were created at both ends, with the most clear-cut opportunity of the half falling to Till ninety seconds before the break.
Taking a through pass from Isaiah Rankin, Till closed in on goal only to be thwarted by a fine tackle from Shrewsbury centre-back Colin Murdock.
Four minutes after the restart, however, it was Shrewsbury who broke the deadlock, Hibbert scoring in fine style as he volleyed home a Darren Moss cross from 12 yards.
Nine minutes later the home side increased their advantage when Ben Herd rolled a centre into the path of Symes who neatly slotted home as Shrewsbury took firm control of the match.
But in the 69th minute Grimsby gave themselves a lifeline. Substitute Gary Jones was sent crashing in the box following a challenge from Herd and Toner converted the ensuing penalty which made for a frantic final 20 minutes, that Shrewsbury , thanks to some determined defending, managed to survive.
In injury time Grimsby defender Ryan Bennett had the dubious honour of being the first player sent off at Shrewsbury 's new stadium – receiving a red card for a second bookable offence.