The home side were ripped apart after half-time and their own play-off hopes are fading after a dismal run of five games without a goal.
Peterborough passed by early chances for George Boyd and Gabriel Zakuani, who failed to hit the target with a header from six yards. Filipe Morais drilled wide for Oldham while Posh's Craig Mackail-Smith should have done better after finding acres of space inside the box.
The visitors broke through after 49 minutes as Boyd seized on poor defending and sent in a left-wing cross which Tommy Rowe calmly slotted into the bottom corner from eight yards.
Rowe turned provider only three minutes later, heading back across goal for David Ball to nod home a simple close-range header. The blitz continued as Zakuani rose unmarked six yards out to head in Grant McCann's corner from the right.
And Mackail-Smith made it four goals in 20 minutes when he raced clean through behind Oldham's defence and comfortably beat keeper Ben Amos from 14 yards. The rout was ended by Mackail-Smith, who hit a stunning volley into the far corner from just inside the box for his 26th goal of the season.