Alan Sheehan's penalty rescued County 15 minutes from time and gave them their reward for a late-season surge in form.
Visiting goalkeeper Bartosz Bialkowski was called into action after just three minutes, parrying a 20-yard shot from Oldham's Gary Harkins.
Another Oldham chance was wasted by Adam Lockwood before Bialkowski produced a fine save from Jonson Clarke-Harris's low drive.
County threatened a breakthrough early in the second half, but Ronan Murray shot too close to Oldham goalkeeper Paul Rachubka who was allowed to save.
Oldham struck after 68 minutes as Harkins delivered a left-wing free-kick and Lockwood headed in from eight yards.
James Dayton was denied by Bialkowski as the home side pushed for a second, but County were awarded a 75th-minute penalty when Jonathan Grounds handled Jamal Campbell-Ryce's cross.
To the delight of over 3,000 away fans, captain Sheehan slammed his spot-kick high into the net.
Oldham went down to 10 men just three minutes later as Lockwood fouled Jimmy Spencer to earn his second yellow card.
Murray forced an impressive save from Rachubka, but the draw was enough for Shaun Derry's side.