Coppinger latched on to a defence-splitting pass from Alun Armstrong to rattle home a low shot in fine style to give Rovers their third win in a row.
The result meant that Oldham's own hopes of making the play-offs were over after a run of six games without a win - and they only had themselves to blame.
Neither side showed much belief in a scrappy first half but Doncaster always had the edge and Coppinger had a goal-bound effort blocked in the eighth minute.
Midfield ace Sean Thornton went close after Danny Hall had made a present of the ball to Lewis Guy who set up the chance ten minutes later.
On-loan striker Luke Beckett toiled in vain for Oldham but he should have scored with a shot on the turn in the 20th minute after latching on to a misplaced clearance but home keeper Alan Blayney foiled him with a fine save.
Richard Butcher was not far off the mark either with a cracking 20-yarder but Oldham's attacks lacked conviction and Doncaster should have been in front at the interval.
But big striker Leo Fortune-West twice missed golden opportunities to break the deadlock before Beckett was unlucky to see a brilliant diving header sail inches over the bar on the stroke of half-time.
It was Doncaster who came out with all guns blazing at the start of the second half and they deservedly snatched the lead in the 66th minute.
Coppinger had led the Oldham defence a merry dance for most of the match and he made no mistake after Armstrong had sent him racing through the middle.
It was poor defending by Oldham and they struggled to rally themselves as heads went down.
The closest they came to an equaliser was in the 81st minute when Chris Taylor swung over a cross from the right to Butcher whose fierce low shot was tipped round the post by Blayney.
Doncaster held out convincingly with Steve Roberts and Graeme Lee twin towers of strength at the heart of the defence to ensure that Oldham went away empty-handed.