The Mariners led from the seventh minute but lacked conviction and Accrington could have been ahead by the interval instead of still trailing 1-0.
But all that was to change within two minutes of the restart when Leam Richardson crossed from the right for top scorer Paul Mullin to head home a simple equaliser.
Poor defending played a big part in that goal and there was a repeat 11 minutes later, when Grimsby failed to clear their lines and Andy Proctor steamed in to rifle the ball home.
Grimsby immediately made a double substitution and switched to a 4-4-2 formation which briefly threatened a revival.
Striker Martin Butler and midfielder James Hunt both forced good saves from keeper Ian Dunbavin who recovered well after a shaky first half.
But the longer the game went on the more obvious it seemed that Accrington would record their fifth away win of the season, for they looked the more dangerous side despite having to defend as Grimsby chased a lost cause.
Things had looked better early on when Grimsby opened the scoring on seven minutes.
It followed a weak punch by Dunbavin and when the ball eventually came to Nick Hegarty he hit home a low shot for his first senior goal for the club.
But Grimsby flattered to deceive and as well as failing to build on that early lead, they looked shaky and hesitant in defence where often trouble was of their own making.
This was a fine result for Accrington, whose away form is excellent and if only they could turn around their home displays they may be in with an outside chance of pushing for the play-offs.