Dale started the game well, with Frankie Connolly heading over and Reece Leonard seeing a deflected shot held by the County goalkeeper.
However, two goals in seven minutes saw the hosts take control of the game.
Firstly, an effort was saved by Dale goalkeeper Jake Braithwaite, with the rebound being slammed home from close range.
The second came when a low cross was also turned home from close range.
After the break, Braithwaite made a superb diving stop to his left to turn away a free-kick, before Dale began to dominate proceedings.
Jake Martyn pulled a goal back with a well-struck effort from just outside the area, which found the bottom corner.
The Dale midfielder was just inches away minutes later, when his driven effort from 25 yards whistled narrowly wide of the upright.
Jaidon Silloway headed wide and Leonard shot over, as Dale went in search of an equaliser.
However, this allowed Stockport to hit them on the counter, and they added a third goal on the breakaway late on to seal the win.
Dale XI | Braithwaite, Bradley, Martyn, Pither, Leonard, Nowacki, Platt, Farrell, F Connolly, H Connolly, Potter.
Substitutes | Gee, Booth, Cunliffe, Williams, Salloway.
