The Sky Blues had the bulk of the chances in the first half but it was the Latics who went in at half-time ahead.
German striker Nick Proschwitz had a hat-trick of opportunities but was twice denied by Oldham keeper Joel Coleman while John Fleck, Jim O’Brien and Grant Ward were all foiled from long range.
Dean Holden’s men had one shot on goal in the opening period and Danny Philliskirk made it count, shooting home from close range in the 13th minute as the home team were caught napping from a quick free-kick.
If Oldham offered little in the first half, it was even less in the second period as Coventry remained camped in the visitors’ half without creating too many clear-cut chances.
Substitutes James Maddison and Simeon Jackson both had half chances but it was big defender Reda Johnson who rescued a point, heading in at the back post from Frank Nouble’s cross from the right in the first minute of injury time.