Rovers won a league match between the sides at the Keepmoat Stadium five days earlier, but they were well beaten on Saturday as Derbyshire ended his nine-match goal drought in style.
Doncaster led after four minutes as Oldham defender Reece Wabara slipped, leaving David Syers to send in a right-wing cross which Robbie Blake controlled before drilling home from 10 yards.
Syers forced a good save from home goalkeeper Alex Cisak but Oldham missed a clear chance when Cristian Montano scooped over from Jose Baxter's through-ball.
Latics hit the woodwork twice, with Montano's fierce drive and Lee Croft's close-range effort both coming back off the bar.
The equaliser came in first-half stoppage time as Baxter delivered a free-kick from the left and Wabara converted a six-yard glancing header.
Oldham deservedly went ahead after 70 minutes when Doncaster keeper Gary Woods saved from Dean Furman and the rebound was snapped up by Derbyshire six yards out.
And they sealed victory seven minutes later after a fine move ended with Furman's left-wing cross to Derbyshire, who stroked a 12-yard finish beyond Woods.