Mariners boss Russell Slade came into the game full of confidence after their Carling Cup win at Derby in mid-week, but it was Paul Fairclough's team who made the early running.
Centre-back Simon King had a good chance in the seventh minute to put Barnet ahead, but his shot went wide of the Grimsby goal.
The home side's energetic midfield caused the Mariners' defence lots of problems with Nicky Bailey and Richard Graham combining well. Grimsby struggled to cope, didn't produce a shot until the 27th minute when Andy Parkinson headed well over from Gary Jones' cross.
But the best chance of the half came five minutes before the break when veteran Ian Hendon raced onto a through ball by Dean Sinclair only to see his shot saved by Steve Mildenhall.
Grimsby shocked the home side just six seconds after the re-start when substitute Calvin Andrew looped a header over the stranded Scott Tynan with his first touch of the match.
Barnet tried to get back into the game but with Giuliano Grazioli looking isolated up front on his own, they struggled to create any clear cut chances.
A succession of corners saw Anthony Charles head well over but it was Grimsby who created the game's next real opportunity when Jean-Paul Kalala Kamudimba fired in a shot from 20 yards which just missed the goal.
As Barnet searched for the equaliser Grimby's Paul Bolland saw red after an altercation with Bailey and he was booked twice in a matter of minutes.
But, despite their numerical advantage, Barnet could not find their was back into the game with Grazioli's header that was cleared off the line by John McDermott being their best chance in the third minute of injury time.