Chris Cornes' 90th-minute strike completed a double for the player on loan from Wolves.
He had originally cancelled out Luke Beckett's fifteenth minute strike. Beckett, who is on loan from Sheffield United, fired home at the near post from Richie Wellens' pass.
Cornes equalised from close range in the 71st minute, but Chris Killen restored Oldham's advantage nine minutes from time after an Andy Liddell corner.
Only for Cornes to have the last say, heading home a cross from former United transfer target George Abbey, and moving Port Vale up two places to 10th.