Tom Youngs scored twice and Nicky Adams hit the third as the Gigg Lane men put themselves out of sight by the break.
Chris Casper had gambled on a young side, but the Shakers started with the same sort of hunger which had seen them sweep aside Championship outfit Sunderland on Tuesday night.
Tom Youngs was preferred to the fit-again Matthew Tipton, and senior stars David Flitcroft and Brian Barry-Murphy were left on the bench. On-loan keeper Kasper Schmeichel replaced Alan Fettis in goal after returning to the club from Manchester City this week.
For Grimsby, a debut was given to new signing Nick Fenton.
Just five minutes in, Adams produced a wicked curling corner from the left and Youngs - making his first start of the season - headed home unmarked from close range.
It was the same routine on 19 minutes when Adams, this time from the left, found the head Youngs at the near post for the Shakers' second goal of the game.
The home side were playing some Champagne football and could easily have had a penalty when Adams was brought down in the area by Tom Newey, only to be booked for diving.
They extended their lead on the stroke of half-time when Adams picked the ball up 35 yards out, drove past Ciaran Toner and smashed a shot into the top corner.
Grimsby introduced Michael Reddy and Peter Beagrie at half-time for the ineffectual Gary Jones and Gary Harkins.
It could have been four immediately after the break when Adams, Youngs and Andy Bishop all rejected the chance to shoot after the Shakers had carved Grimsby up once more.
Peter Bore, one of the only Mariners men to have done himself justice in the opening hour, went close with a rasping drive on 54 minutes with Schmeichel beaten.
Fifteen minutes later, Youngs nearly claimed his hat-trick when he failed to direct yet another poorly-defended corner towards goal.
Bury looked content to settle for a three-goal lead and allowed Grimsby far more possession in the final quarter of the game.
As a result, Reddy hit the sidenetting with a header and Paul Scott was forced to clear a Justin Whittle cross from on his own goal line.
But on the rare occasions they decided to stretch their legs, they still proved a threat to Graham Rodger's side.