An own goal from James Tarkowski and Steven Schumacher's late penalty handed the Shakers all three points as they continued their revival under new boss Kevin Blackwell.
Bury almost grabbed an early lead when Tom Hopper's header brought a fingertip save from Latics keeper Dean Bouzanis. The breakthrough did come after 34 minutes as Matt Doherty crossed from the right and Cliff Byrne's defensive header cannoned into team-mate Tarkowski before dropping into the net.
The hosts had a penalty appeal waved away on 65 minutes after substitute Dean Furman was felled by loanee Zac Thompson, while visiting keeper Trevor Carson denied Jose Baxter and Matt Smith.
However, Bury sealed the points four minutes from time when Tarkowski tripped David Worrall, with the resulting penalty hammered into the roof of the net by Schumacher.
Oldham's consolation came deep into stoppage time, with Robbie Simpson meeting Lee Croft's right-wing free-kick to score with a deflected eight-yard header.