Grimsby remain in danger of relegation as Accrington ensured their survival with a goal from Michael Symes.
Symes, on loan from Shrewsbury, broke the deadlock after 71 minutes with a close-range header that leaves Grimsby just a single point from the drop zone.
John Miles and Peter Cavanagh both went close for Stanley in the early minutes.
Accrington keeper Kenny Arthur was kept busy in the second half, coping with a close-range effort from Barry Conlon and a curler from Nick Hegarty.
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