The Cumbrians kicked off with hope of grabbing sixth spot, but even a Boundary Park victory would not have been enough due to the results at Notts County and Stevenage.
Carlisle wasted two first-half chances as Paddy Madden blazed wide and Jon-Paul McGovern scuffed off target when unmarked 10 yards out. But Oldham were also a threat, with Kirk Millar's chipped shot drifting just over before defender James Tarkowski headed against the crossbar.
Tarkowski scored four minutes after the break as he met Reece Brown's long throw-in with a looping header which beat 'keeper Adam Collin from 10 yards.
Shefki Kuqi could have doubled Oldham's lead but Carlisle levelled after 68 minutes when McGovern crossed from the right and substitute Tom Taiwo planted home an eight-yard header.
But Oldham snatched the winning goal - and their first victory in nine games - just four minutes later, Filipe Morais delivering a right-wing corner for substitute Oumare Tounkara to head in from six yards.