Liam Trotter and Nathan Jarman scored twice in seven minutes to give the Mariners a deserved 2-0 lead inside 22 minutes.
And although Mike Newell's men lost Jean-Paul Kalala to a second yellow card in the 36th minute, Bury were unable to avoid their fifth straight home defeat.
Grimsby could have opened the scoring as early as the fourth minute, but Nick Hegarty hesitated, allowing Efe Sodje to get back and block his shot.
Sodje was then fortunate not to be penalised for bringing down Adam Proudlock when through on goal, with Proudlock and Kalala being booked for their protests.
Jamie Clarke then tested Bury keeper Wayne Brown at his near post, before the Mariners grabbed a deserved lead.
Tom Newey's left-wing cross looped up off the head of defender Ryan Cresswell and Trotter was on hand to head home the loose ball from two yards.
The visitors quickly doubled their lead with Jarman getting in behind Sodje to turn Clarke's right-wing cross inside the far post.
And Grimsby almost scored a third as an unmarked Rob Atkinson headed straight at Brown from Newey's free-kick and Ryan Bennett failed to force in the rebound.
Andy Morrell and Stephen Dawson headed over as Bury made a positive response and their cause was helped when Kalala was shown a second yellow card for a foul on Paul Scott.
Chris O'Grady, a surprise inclusion ahead of Bury's top scorer Andy Bishop, then clipped the crossbar from a wide angle.
Bishop replaced Morrell at the interval and he and O'Grady fired narrowly wide as Bury made a lively start to the second half.
Grimsby enjoyed some respite as Trotter tested Brown from distance, although Mariners keeper Phil Barnes then had to make a fine save to deny Dawson.
Barnes denied Dawson again while sub Glynn Hurst volleyed wide late on as Grimsby sealed their first win in 23 league games, a run stretching back to March.