The Stags have suffered six consecutive defeats in League Two but top scorer Sam Clucas hit a fine equaliser at Boundary Park, registering his fifth FA Cup goal of the season having bagged four in the club's 8-1 first-round success at St Albans.
Mansfield made the brighter start and wasted a chance when Clucas glanced wide from Lindon Meikle's cross.
Oldham then went ahead with a stunning 28th-minute goal from captain Korey Smith, who burst down the left wing, cut inside and bent his shot into the top corner from 16 yards.
John Dempster headed off target for Mansfield but they equalised in the last minute of the first half when Clucas lashed home a superb free-kick from just outside the penalty area.
The hard-working visitors could have snatched the lead after 54 minutes only for Martin Riley to miss the target from close range.
Mike Petrasso and Jonson Clarke-Harris had Oldham's best chances to find a winner but they were both easily saved by Mansfield goalkeeper Alan Marriott.