Improving Rovers, who had won four of their last five matches before Saturday, almost held on for their first away clean sheet of the season at Edgeley Park.
But Stockport's Tanto Olaofe headed home the winning goal in the 83rd minute after he was left unmarked in the six-yard box.
The defeat was a little harsh on Doncaster, who held their own for large parts.
Scroll down for our player ratings.
9. Zain Westbrooke - 7
Again very good for large periods as Doncaster almost upset the script. Neat and tidy in possession and helped get his side moving up the pitch. Never afraid to get on the ball from deep. Photo: HOWARD ROE
10. Tommy Rowe - 6
Looked to be in a running battle with Antoni Sarcevic, one of many danger men for Stockport. Faded as the game wore on before being replaced. Photo: Bruce Rollinson
11. Joe Ironside - 6
Missed a great chance to score but did appear to be off balance. Led the line well at times without seeing many opportunities fall his way. Photo: Bruce Rollinson
12. Mo Faal - 6
Saw an overhead kick fly wide late in the first half, when he was excellent in possession, using his obvious ability on the ball to drive forward. Quieter after the break, however. Photo: Howard Roe/ahpix.com