Jimmy Smith put the O's ahead early on but Kirk Millar equalised for the visitors shortly after half-time.
Only 10 minutes had been played when Smith raced into the penalty area to meet a deft flick by Charlie MacDonald before sending his first-time lob over advancing goalkeeper Dean Bouzanis from 15 yards.
However, the Latics had already forged two openings by then with Korey Smith and Lee Croft both missing out with shots that only narrowly cleared the target.
The second half was just 50 seconds old when Oldham got themselves back on level terms.
The home defence failed to deal with a cross by Cristian Montano and the ball dropped into the path of Millar who applied the finishing touch, with his shot rolling over the line off the inside of the right-hand post.
With five minutes remaining substitute Lee Cook picked out Dean Cox with a superb cross-field pass but the O's midfielder squandered the opportunity of taking all three points for his side when he crashed his shot against the upright from eight yards out.
Oldham introduced 16-year-old Jack Truelove for his first taste of league football while 18-year-old Harry Lee made his league bow for the O's from the bench.