Denis Smith's Dragons took a 2-0 lead into the break after Chris Llewellyn opened the scoring for the visitors on 19 minutes before Steve Thomas doubled their advantage five minutes later.
Chris Armstong made it 3-0 on 63 minutes before The Mariners replied with a consolation strike from Phil Jevons ten minutes later.
The result keeps the North Wales club's push for a play-off place very much alive while Grimsby remain just four points above the Second Division drop zone.
Click below for a match summary:
Division Two
Grimsby 1-3 Wrexham
Click here for an updated Division Two table.
