Gary Johnson's men fell two goals behind for the second successive London Road outing, but just as against Huddersfield last time out, they roared back with a high-class attacking onslaught on Saturday.
Ritchie Jones headed the visitors into a 20th-minute lead after climbing above Tommy Rowe to meet a volleyed left-wing cross from Paul Black and register his first Latics goal. Athletic doubled their lead seven minutes before the break courtesy of Chris Taylor's back-post header after Kieran Lee had delivered from the right.
But the turning point arrived on the stroke of half-time when James Wesolowski nodded in a Tommy Rowe cross to launch the Posh fightback. After tempers had threatened to boil over following a clash between Lee Tomlin and Jones on the hour, Peterborough went on to take control.
Aaron Mclean hauled the hosts level by glancing in his sixth of the season from Chris Whelpdale's long throw in the 62nd minute and George Boyd completed the transformation in the 71st minute when he robbed Lee and rifled a low 15-yard shot past keeper Dean Brill.
Substitute Dave Hibbert wrapped up the points by diving in to head his first Posh goal from Grant McCann's 82nd-minute corner. And McCann rubbed salt into Oldham's wounds with a stoppage-time penalty after Reuben Hazell had fouled Boyd.