Former Sky Blue Jonson Clarke-Harris came back to haunt his former club and his header gave the Latics the lead right on the stroke of half-time. But Baker's strike ensured it ended all-square at Sixfields.
It was Coventry who had the better of the opening exchanges and they were unfortunate as Callum Wilson raced through one-on-one only to be brought down outside the area by visiting goalkeeper Mark Oxley.
Referee Dean Whitestone controversially issued a yellow card and the visitors made the most of their good fortune when Clarke-Harris scored his fourth goal in as many games against the run of play.
But City replied in spectacular fashion after the interval, and after 73 minutes they were rewarded for their constant pressure when Cyrus Christie's cross from the right was turned in by Baker.
However, Oldham could have snatched all three points right at the death but Michael Petrasso's effort was well saved by Joe Murphy.