But it was scant consolation for the north London side, who were comprehensively out-played and, but for some good saves by goalkeeper Lee Harrison, could have fallen to a much heavier defeat.
Grimsby put behind them the trials of last Friday's home defeat by MK Dons after making a bright start and they only fell away in the second half with the game already in the bag.
With big strikers Martin Butler and Gary Jones causing problems for the Barnet defence, it looked only a matter of time before the Mariners broke through.
But it was at 29 minutes on the clock when their good work was finally turned into goals.
Wing-back Nick Hegarty played a neat one-two with Butler and finished coolly with a low shot.
But just when it looked as though Barnet might reach the interval only one goal in arrears, they conceded a bad second on 43 minutes.
Defender Ryan Bennett headed on a Rob Atkinson throw-in for Butler to lash his shot into the net from close range.
Barnet did open the second half rather brighter, but a terrible mistake by Nicky Nicolau let in man-of-the-match Paul Bolland and the midfielder ran through before finishing like a striker.
Grimsby got a little sloppy at times after this and Albert Adomah had two or three chances before Cliff Akurang headed in from close range on 80 minutes.
For a few minutes it looked as though Barnet might just get back into the game but substitute Andy Taylor put the result beyond doubt on 85 minutes.
He ran through and finished brightly to make it 4-1.
Grimsby, who now have 52 points, face successive away games at Darlington and Mansfield which could enhance their play-off chances.