The home side created two decent chances inside the opening eight minutes.
First Adam Griffin turned inside but saw his shot saved by Posh keeper Mark Tyler, before Matty McNeil dived in only for Tyler to again come to the rescue.
McNeil then launched himself at a Griffin in-swinging corner-kick, but his header was off target.
On 13 minutes, Peterborough responded when skipper Chris Westwood rifled in a 35-yard drive, but Stockport keeper Conrad Logan superbly tipped the ball over for a corner.
Peterborough opened the scoring on 15 minutes. McLean flicked the ball into the path of strike partner Craig Mackail-Smith and he volleyed home in style from ten yards.
Stockport levelled matters on 22 minutes with a simple goal. Centre-back Craig Morgan failed to clear Jason Taylor's long throw-in and McNeil comfortably headed the loose ball past Tyler.
Six minutes before the break, Stockport were denied when Tyler expertly beat away a powerful drive from Adam Proudlock, but in first-half stoppage time it as the visitors who re-took the lead.
Jamie Day threw in to McLean and he smashed home a mesmerising effort from 25 yards right into the top corner.
In the second half, Tyler got down well to palm away Taylor's well-hit low drive, then County substitute Liam Dickinson somehow scooped a shot over from just eight yards.
Stockport's leading scorer Anthony Elding saw a goal chalked off for offside on 69 minutes, then as time ran out, substitute Greg Tansey shot narrowly wide.