Goals from Tom Hopper and David Worrall sent Pools to the foot of the table as Neil Austin missed a late penalty.
Both teams created a host of chances, a nervy Trevor Carson scrambling to save Ritchie Humphreys' free kick, while in the opposite goal Scott Flinders was equally determined, beating out a powerful Steven Schumacher free-kick before denying Worrall one-on-one.
But Hopper broke the deadlock eight minutes before the break, applying the finish to a low cross from on-loan Leeds teenager Dominic Poleon.
Ryan Noble scooped a shot over the crossbar from six yards, while Andy Bishop too missed a sitter, heading Peter Sweeney's cross wide.
Bury extended their lead through a superb strike from Worrall only for Noble to peg them back again with a stunning 30-yard volley.
Pools defender Sam Collins cleared off the goalline from David Healy, but the visitors could not take advantage and Austin slammed his spot kick against the crossbar after Noble had been fouled.