The game was settled with a goal three minutes into the second half, while Wanderers were reduced to ten men when Turkish midfielder Akin Bulent was sent off for a second bookable offence and it was no more than the side who nearly went out of business last season deserved.
They had all the goal chances while a Wanderers side showing ten changes from the line-up that drew with Southampton in the Premiership four days ago, hardly troubled the Shakers keeper Glynn Garner in the whole of the 90 minutes.
Bury had enough of the play in the first half to worry the Premiership side, Jon Newby, Pawel Abbott and Terry Dunfield all found themselves with good chances, but off-target shooting meant that Kevin Poole in the Wanderers goal was seldom troubled.
Yet their efforts were more than the Wanderers could produce and Chris Armstrong and Jonathan Walters were given little chance to shine up front.
In fact the home side failed to put a worthwhile shot at goal in the first half while Bury were the side that made all the chances.
That pressure finally paid off three minutes after the restart and it was the hard working Newby who set up the goal.
He carried the ball into the penalty area before sweeping it across the face of goal from where Bernard Mendy slid the ball into the net under the challenge of Colin Woodthorpe.
Minutes later Newby set up another good chance, but this time Dunfield fired over the goal.
Wanderers immediate reaction was to bring on Dean Holdsworth, Henrik Pedersen and Kevin Nolan in place of Armstrong, Walters and Jermaine Johnson, but their cause was not helped when Bulent was sent off in the 64th minute after collecting his second yellow card.
Bury were enraged when the fourth official showed six minutes of injury time to be played yet it gave them a chance to pile on more pressure and misery for Wanderers.
Chris Billy blazed the ball over the bar after creating a clear cut opportunity.