The £20,000 signing found himself unmarked at the far post following Sam Igoe's corner to volley home his first goal for his new club just 14 minutes into the game.
It could have been a different story if Oldham defender Will Haining had connected with his header just 90 seconds into the game after David Eyre's free-kick.
The Latics defender was completely unmarked just two yards out but failed to make any contact as the ball sailed out for a goal kick.
After Roberts' goal, man of the match Brian Howard went close twice before the break.
His first effort, a 25-yard left foot shot, was turned round the post by keeper Leslie Pogliacomi before the giant Aussie denied Howard again seconds later with another routine save.
Oldham's best chances fell to striker Scott Vernon who was recently recalled from a loan spell at Blackpool.
Vernon got free in the box and fired goalwards on 50 minutes only to see keeper Rhys Evans palm the ball over the bar.
Just six minutes later Evans was again called into action as he sprinted from his line to deny Vernon with a super reflex save after the striker sprung the offside trap.
Swindon midfielder Igoe rattled the outside of the post midway through he second period after great work by Rory Fallon.
Oldham substitute Christopher Hall almost snatched an undeserved point for the visitors 15 minutes from time.
Hall saw his shot from the edge of the box deflect off Sean O'Hanlon and sail inches over the bar.