Claude Gnakpa scored the game's only goal as Luton Town extended their unbeaten league run to nine matches.
Gnakpa broke the deadlock, planting Alex Lawless's pinpoint left-wing cross home from six yards.
The Mariners came close to levelling through Serge Makofo's stinging drive, which forced a fine save from Hatters goalkeeper Mark Tyler.
The away team nearly grabbed a point at the death, Alan Connell's 20-yard curling shot flying inches wide.
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Luton: Tyler, Gleeson, Pilkington, Kroca, Howells, Gnakpa, Keane, Lawless, Drury, Owusu, Barnes-Homer (Walker 76). Subs Not Used: Asafu-Adjaye, Crow, Poku, Watkins.
Booked: Lawless.
Goals: Gnakpa 25.
Grimsby: Arthur, Watt (Garner 74), Kempson, Atkinson, Wood, Bore, Leary (Sinclair 58), Cummins (Hudson 74), Eagle, Makofo, Connell. Subs Not Used: Croudson, Corner.
Booked: Kempson, Atkinson, Garner.
Att: 5,609
Ref: Kevin Johnson (Somerset).
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