Victory moved the Cumbrians above the 50-point barrier, but the Latics remain in deep trouble after their first defeat under new manager Lee Johnson.
Carlisle broke through after nine minutes when Oldham lost the ball cheaply in midfield and Liam Noble advanced before slamming home a shot from 20 yards.
The away side were in total control and made it 2-0 after 33 minutes as Noble's throughball found overlapping full-back Jordan Mustoe, who superbly lobbed goalkeeper Dean Bouzanis from the edge of the box.
Oldham posed their first threat shortly before half-time, Jose Baxter's powerful shot forcing a save from Mark Gillespie.
A treble substitution brought the Latics to life, but Matt Smith's header was hacked off the line by Peter Murphy.
Oldham grabbed a 73rd-minute lifeline as Mustoe tripped Korey Smith inside the box and Baxter sent Gillespie the wrong way from the penalty spot.
Baxter, Matt Smith and Bobby Reid all had good chances to equalise, but Gillespie was in inspired form and Carlisle held on.
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