It may have taken a late penalty to secure the three points but in doing so they moved three points clear of second from bottom Chester City.
Squally windy conditions meant that the game was never going to be a classic and the wind had the biggest influence on the 90 minutes.
But there was no faulting the honest endeavour of both teams who did try to play football in the difficult conditions.
Aldershot started brightly and had a couple of good efforts from distance before midfielder Kirk Hudson had the best chance of the first half on 30 minutes only to be denied by a smart save from keeper Wayne Henderson.
The first half play was pretty even but Grimsby took a grip after the break and substitute Peter Bore went close on the hour with a terrific 25-yarder that clipped the top of the bar as it flew behind.
It looked more and more obvious that one goal would decide it and that would probably come from an error.
As the game moved into its final ten minutes the Shots looked on course for only their second away draw of the season.
But then skipper Anthony Charles tangled with Mariners striker Barry Conlon and the referee pointed to the spot.
Aldershot protested but Conlon grabbed the ball and coolly despatched his spot-kick down the middle to give Grimsby the lead.
Two minutes later Nick Hegarty had the ball in the Aldershot net again but it was ruled out for a foul.
There were four minutes of stoppage time but Grimsby held on without too much fuss for a deserved victory.