John Sheridan's side hit the front at the ABAX Stadium as Lee Erwin struck for the third time in two games.
The Leeds United loanee volleyed in an Oliver Banks cross after 11 minutes to make the most of a rare Oldham attack in a first half dominated by the hosts.
They succeeded in holding onto their advantage until the 73rd minute when two Posh replacements combined to great effect.
Half-time arrival Marcus Maddison delivered a stunning cross from the left which was headed in by Junior Morias, who had been brought on after an hour.
Former non-league hot-shot Morias was a whisker away from completing a rapid turnaround when firing just wide four minutes later.
Oldham then ended the game on the attack as substitute Temitope Obadeyi was thwarted by a Jack Baldwin recovery tackle before Anthony Grant bravely blocked as Aiden O'Neill came close.
The deadlock left the Latics three points above the relegation zone.