Grimsby dug deep to record their first league win of the season despite spending most of the game with 10 men.
Liam Trotter and Nathan Jarman put the Mariners two up early on before Jean-Paul Kalala was shown a second yellow card in the 36th minute.
Robert Atkinson should have scored a third Grimsby goal but headed straight at keeper Wayne Brown.
Stephen Dawson twice went close to scoring for Bury, but they were unable to avoid a fifth straight home defeat.
Grimsby: Barnes, Stockdale, Bennett, Atkinson, Newey, Clarke, Kalala, Trotter, Hegarty (Boshell 61), Proudlock (North 88), Jarman (Bore 68). Subs Not Used: Hope, Montgomery.
Sent off: Kalala (36)
Booked: Kalala, Proudlock.
Goals:Trotter 17, Jarman 22.
Att: 2,549
Ref: Graham Laws (Tyne & Wear).
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