Posh did equalise in-between strikes from Scott Vernon and Neil Kilkenny, but their miserable away run went on while Oldham stretched an unbeaten record at Boundary Park which goes back to October.
An error by Mark Tyler cost Peterborough what turned out to be the winning goal, although boss Barry Fry later defended his keeper saying: "We would have been relegated already this season if it had not been for Mark."
Posh also lost Gareth Jelleyman to a hamstring strain whereas Oldham enjoyed a happier day by giving themselves a healthy gap above the drop zone.
The game started poorly with only a couple of half chances which were wasted by Oldham's Kevin Betsy and Peterborough wing-back Jelleyman.
Oldham manager Brian Talbot made an inspired substitution at half time as Vernon made an instant impact by putting his side ahead.
Kilkenney helped on a free-kick by Danny Hall and Vernon brought down the ball 12 yards out before slotting it past Tyler.
But Posh were level within two minutes as a trademark Andy Legg long throw was flicked on at the near post and Richard Logan crashed in the ball from close range.
Posh were level for only six minutes as Tyler ran off his line to claim a cross but could not hold on as he fell to the ground.
Kilkenney seized on the chance 10 yards out and fired his shot into the top corner with his right foot.
The visitors almost equalised when Craig Ireland saw his header cleared off the line by Adam Griffin but they mustered few other chances.