The winning goal was a scrappy one in keeping with an awful game. In the 44th minute, Barnet broke down the right and a cross from Albert Adomah was bundled past keeper Phil Barnes by midfielder Neil Bishop.
Despite the referee playing nearly six minutes of added time in the first period, there was no reply from the home side and it wasn't until the 83rd minute that they finally managed a shot on target.
Malvin Kamara tested keeper Lee Harrison with the effort producing ironic cheers from the long-suffering home supporters.
A goal to the good, Barnet had no real incentive to push forward in the second half and by defending in-depth they gave Grimsby little chance to break them down.
Having said that, there was little spark or inspiration from the Mariners, who have scored only three goals all season.
At least Paul Fairclough, the Barnet manager, was happy to see his side's first win of the season, which was just about deserved, for they did carry a little more goal threat than the home side.
It is just fortunate for these two struggling teams that the three teams below them in the table all started with points deductions, although the margins are getting reduced as each game goes.
It was a happy journey back to north London for Barnet's 81 travelling fans, who got right behind their side and celebrated at the end of the game as though they had won promotion.