With ace striker Lee Trundle kept in check by Guy Branston it was the second match in succession the Swans failed to score.
Swansea had Sam Ricketts back as one of three changes following the defeat at Yeovil, which had knocked them off the top of League One.
The visitors dealt with an early Swansea raid before forcing a couple of corners and Willy Gueret was the busiest man on the field in the early stages.
The Swans responded in the 11th minute when Trundle crossed from the left but Marcus Bean headed wide when well placed.
Bean had another chance midway through the first half and brought a diving save from Oldham goalkeeper Chris Day, after Trundle had made space down the left.
As the first half drew to a close Marc Goodfellow weaved his way into the danger area but his low shot was way off target.
Adrian Forbes replaced Goodfellow at the start of the second half and he was quickly in the action flashing in a shot as the Swans made the early pressure.
They almost took the lead on the hour when Trundle won a free-kick. Skipper Roberto Martinez floated the ball towards goal and Izzy Iriekpen leapt high to head for the corner, but the ball drifted just wide of Day's far post.
Andy Robinson was brought on to add some firepower to the shot-shy Swans and he brought Day to his knees when he rifled in a long range effort.
Another chance went begging when a Ricketts cross was headed high over the bar by Iriekpen as the Swans kept the visitors locked in their own half in the final ten minutes.
Both sides had chances in time added on but a draw was a fair result in a scruffy game neither side deserved to win.