Bury had to settle for a 0-0 draw at home to a Plymouth side also in Sky Bet League One's relegation zone.
The hosts dominated and hit the woodwork three times in the second half.
But Argyle hung on to halt a four-match losing streak and leave Bury seven without a win.
Striker Michael Smith had most of the hosts' chances, hooking an early Chris Humphrey cross over.
Josh Laurent twice tested Luke McCormick from distance while Argyle replied with Jamie Ness and Nadir Ciftci going close.
Smith then headed wide while team-mate Nathan Cameron turned Smith's shot straight at McCormick.
The second half began with Smith seeing a low shot saved and Chris Maguire nearly caught out McCormick from a tight angle, with the Argyle keeper tipping his free-kick onto the bar.
Bury brought on Bournemouth loanee Mihai Dobre and the Romanian winger crossed for Smith to sidefoot against the far post.
Dobre then fired straight at McCormick before cutting inside and seeing the Argyle captain turn his shot against the post.
McCormick then denied Dobre again at the death and Laurent's follow-up was blocked by Gary Miller.