Pools jumped over their opponents at the foot of the table thanks to two goals from Andy Monkhouse and are now five points from safety with three games to go.
John Hughes' side were never troubled against a desperate Bury, who appear set to join Pools in League Two at the end of the season.
Pools midfielder Simon Walton hit the post after five minutes, but the home side had to wait until two minutes before half-time to score.
Jon Franks' corner was headed over the line by Monkhouse and it was Pools' first goal in 762 minutes, since Monkhouse scored against Crewe on February 26.
The Shakers had Craig Fagan sent off for a foul on Darren Holden before half-time and there was still time for Franks to miss an open goal before the break.
Andy Bishop had the visitors' best effort, holding off Jack Baldwin and curling over after 55 minutes.
But the game was won in the 72nd minute when Franks crossed from the right and Monkhouse's near-post header crept over the line.