Substitutes Richie Baker and Andy Mangan grabbed the goals that ensure the Shakers continue their steady climb up the table.
It was a match that promised much, Bury unbeaten in five at home and promotion-chasing Posh enjoying a run of six games without defeat.
But, although there was plenty of decent football on display, it didn't really deliver during the opening stages.
The first effort of any note only came 22 minutes in and that was a speculative effort from Baker which went straight into the hands of Mark Tyler.
Peterborough's attacking triumvirate of George Boyd, Aaron McLean and Craig Mackail-Smith always looked dangerous with the ball at their feet, they just didn't see enough of it.
Meanwhile, Bury went quietly about the task at hand and finally broke the deadlock 32 minutes in. Paul Scott found Baker inside the area and he quickly shifted the ball on to his right foot before finding the corner.
Peterborough were a completely different side after the break, however, and quickly forced themselves onto the front foot.
Mackail-Smith fired into the sidenetting from close range, while Charlie Lee's header was cleared off the line by Steve Haslam, amid serious appeals that the ball had already entered the net.
Aaron McLean and Micah Hyde both flashed efforts wide of the post and an equaliser seemed almost inevitable.
But Bury weathered the storm and struck out on the break six minutes from time. Andy Bishop raced clear of the defence and fed Mangan, who had a simple finish to complete the win.