The Bees went into the game with an unchanged line-up but conceded early when Danny Collins hit a 6th minute corner past Craig Ross.
After an end-to-end start, the game became a tighter encounter and the next clear-cut opportunity came in the 21st minute when Nelson’s header from Watson’s corner was kept out by McKeown.
After the break, Barnet were looking a lot more dangerous and tied the game just after the hour mark when substitute Jean-Louis Akpa Akpro hit a shot low past McKeown.
The Bees continued to press, Richard Brindley trying his luck from the edge of the box but firing wide of target.
With a little over 10 minutes left of the 90, Barnet took the lead when Curtis Weston popped up with his first goal of the season, cutting inside before firing home.
Grimsby were given the opportunity to level almost immediately however when Jackson was brought down in a group of bodies.
Mitch Rose stepped up to take a hit the ball to the right of Craig Ross who went the correct way but couldn’t keep it out.
Attendance- 5,416 (123 Barnet fans)
Barnet: Ross, Brindley, Nelson, Watson, Weston, Akinde, Coulthirst, Tutonda, Kyei (Clough 35’), Nicholls (Akpa Akpro 59’), Sweeney.
Unused subs: K. McKenzie-Lyle, J. Taylor, Fonguck, Shomotun, Payne.