Mark Gillespie made a string of fine saves to preserve the Cumbrians' lead after they took control at Boundary Park with goals from Liam Noble and Jordan Mustoe.
Gillespie's heroics began just before half-time when he tipped away Jose Baxter's stinging drive.
Oldham were transformed by a treble substitution at the break, but Matt Smith and Bobby Reid were both denied by superb saves.
The home side's only consolation came after 73 minutes as Korey Smith was brought down by Mustoe, allowing Baxter to send Gillespie the wrong way from the penalty spot.
Carlisle boss Abbott said: "Mark Gillespie made a mistake a couple of games back, but I stuck with him. He has come back well and he made some great saves. He was really outstanding.
"We think he's a good young goalkeeper and that performance will have done his credentials the power of good.
"We are absolutely delighted with the result because this was always going to be a hard game. Oldham are fighting for their lives and take advantage of having some big lads, so we had a job to do defensively.
"We had to dig in when Oldham bombed it forward, but overall we should be proud of the performance.
"We are picking up good results in difficult games. We are on a little run and want to end the season as powerfully as we can."
- Sports & Recreation
- Jose Baxter