Joe Garner scored twice for Carlisle, who won at home in League One for only the second time this season to end Oldham's four-match unbeaten run.
The hosts went ahead when Liam Noble crossed for an unmarked Garner to head home from close range.
The striker nodded in Matty Robson's delivery for 2-0 and Robson pounced on a loose ball to seal the game.
Jose Baxter netted a late consolation from the penalty spot for the visitors after Matt Smith was fouled in the box.
VIEW FROM THE DRESSING ROOM
Oldham manager Paul Dickov told BBC Radio Manchester:
"We knew coming up here that it was going to be tough. For whatever reason, I thought we were very flat-footed and lethargic.
The desire and the workrate to win football matches that we've had didn't seem there tonight.
"When you're not playing well, it's important that you grind out a result.
"We were thinking it had 0-0 written all over it, but individual errors cost us for all three goals."