This was an opportunity to put pressure on their League One promotion rivals but manager Phil Parkinson was left frustrated as his side failed to score for the third game in succession.
The Addicks started well and came close after 11 minutes as Nicky Bailey sent a shot just wide, before Miguel Angel Llera tested visiting goalkeeper Dean Brill with a long-range drive that was pushed wide.
Dean Furman curled a shot wide from the edge of the penalty area for Oldham following a period of neat passing.
Therry Racon had the first opportunity of the second half for Charlton as his shot was blocked at the near post, but Oldham then took the initiative.
Striker Pawel Abbott had a goal ruled out after 52 minutes due to a foul in the build-up to his close-range tap-in, and then Keigan Parker sent a shot high and wide.