The home side had the better of the first half and almost went in front when Connor Brown’s 20-yard drive had to be turned round the post by Chesterfield keeper Tommy Lee.
Lee also made a flying 29th-minute save from Rhys Murphy as the Oldham striker connected with an acrobatic overhead kick.
Centre-back Charlie Raglan had a half-chance for Chesterfield, but his shot was comfortably saved by Latics keeper Joel Coleman.
Jimmy Ryan and Ian Evatt both went close as the Spireites, boasting five wins in their previous six games, began to take a foothold.
They created their best chance in the 82nd minute, but Armand Gnanduillet blazed over from close range after a Sam Clucas flick came back off the post.
There was still time for Clucas to again threaten a winning goal, only for Coleman to make a fine save from his dipping 20-yard shot.