Hartlepool saw off Bury to move to within five points of the League One play-off places.
Ritchie Humphreys gave Pools the lead in first-half injury time with a header from Neil Austin's cross.
Adam Boyd slammed home Andy Monkhouse's flick-on to double their advantage.
David Worrall gave the Shakers hope with a delicate lob over Scott Flinders with 11 minutes remaining but they could not manage a leveller despite two late penalty appeals.
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Hartlepool first-team coach Neale Cooper tells BBC Tees:
"The important thing was that we bounced back tonight, to come here and do that I was pleased with the outcome.
"They were superb tonight, they defended well when they had to defend.
"Even at the end when they were coming at us, the shape was good and Scott Flinders kept the back four out high.
"I got a bit of stick from their fans but that's part of the game."