Grimsby bossed the first half and took a deserved lead, but they then had to withstand some heavy Wrexham pressure before tying up the points with a second goal three minutes from time.
All eyes were on Grimsby to see how they would react after last week's 5-0 pasting at County neighbours Lincoln.
And, although it wasn't a vintage performance, they showed just enough determination to take three points.
Because of injury and illness both sides had to make changes with Wrexham expected to show some ill effects from a gruelling Welsh cup tie against Swansea in midweek.
And it was Grimsby who enjoyed the first half and took a deserved lead on 24 minutes. Skipper Justin Whittle returned the ball into the middle when a free-kick was only half cleared and Gary Jones controlled it before blasting his 13th goal of the season past Wrexham keeper Michael Ingham.
Wrexham came out for the second half in determined fashion and pushed Grimsby back. They went closest to an equaliser when a Matt Crowell free kick from 25 yards was spectacularly fisted away by Grimsby keeper Steve Mildenhall.
But in the closing stages, as Wrexham pushed more and more men forward for the equaliser, they were caught out at the back when striker Michael Reddy went through but still had to do a lot of work before putting his shot past Ingham.
That came with just three minutes left and, even with another three minutes of added time; Wrexham could not get back into it.
The defeat for Wrexham means their play-off hopes are hanging by a thread while second place Grimsby can go to leaders Carlisle next Saturday full of confidence. And with just six games left for the Mariners automatic promotion is well within their grasp.