The Latics had a nightmare at the back and could find no way of recovery after they gifted first-half goals to Kayode Odejayi and John Finnigan.
Oldham keeper Les Pogliacomi was taken off at the break and his replacement, Alan Blayney, had to make some impressive saves to prevent Cheltenham running up a bigger victory.
The result was a major blow to Oldham as they bid to cement a place in the play-offs, but Cheltenham have opened up a healthy gap above the bottom four.
The visitors took the lead after 22 minutes after a cross from the left caused chaos in Oldham's back line and was not cleared.
The ball rebounded to Odejayi on the edge of the six-yard box and he tucked in a simple finish for his 14th goal of the season.
It was soon 2-0 as Oldham conceded a corner and again found themselves in all sorts of trouble when they tried to clear the danger.
Pogliacomi tried unsuccessfully to get his hands on the ball but was left in no-man's land when Robins captain Finnigan lifted it back over his head and underneath the crossbar from 18 yards.
Finnigan's goal was superbly taken and Cheltenham would have added a third before half-time but for Pogliacomi's save from Odejayi.
The home side rallied after the break and Chris Porter was denied by a superb block from Shane Duff, before Gary McDonald fired his shot inches wide of the far post.
Oldham's challenge was seen off by excellent Cheltenham defending and it was the Robins who were the more dangerous team in the final half hour.
Substitute keeper Blayney thwarted Finnigan and then made a brilliant late save from John Melligan.