The Hatters' bid to close in a top-three place was hit by an early penalty and they then went two down in the second half, before so nearly claiming a point with a late fightback.
The penalty after 14 minutes came in Rovers' first threat on goal. Rickie Lambert saw his near-post blast beaten away and as he chased the rebound he was fouled by Michael Rose.
He took the kick himself, thumping it high and straight as keeper Wayne Hennessey went to his left.
For the rest of the half Rovers were left snatching at chances, the best of them two efforts by young on-loan striker Stuart Nicholson.
A quick covering Stockport defence gave them few opportunities, while in attack the visitors were always posing problems for a makeshift home defence.
Sam Oji, on loan from Birmingham, found the task of keeping Stockport's top scorer, Anthony Elding, beyond him.
He so nearly gifted County a goal when he sent a header straight to Elding, whose volley flew past the left-hand post.
With David Poole and Adam Le Fondre adding pace to Elding's power, Steve Phillips in the Rovers goal had a busy night.
His catching was sometimes uncertain, notably when he missed a cross from Rose, whose overlapping run carried him to the byline.
The cross should have been cut out by Phillips but was finally scrambled away at the far post.
A keen first half saw both team bosses Paul Trollope and Jim Gannon in touchline spats with officials, but the game then drifted until Nicholson brought it back into focus on the hour.
A header from Lambert put Craig Disley clear and after his shot came back off Hennessey, Nicholson was there to hammer in the rebound.
There was confusion, though, for Stockport's lone reply, Rose's near-post corner finally being fumbled over the line by keeper Phillips.