The hosts got themselves off to a dream start as they took on one of their rivals in the push for a play-off place.
Inside three minutes Anthony Elding was barged over by Robbie Williams, and County left-back Michael Rose curled home a superb 20-yard free-kick.
Adam Griffin hooked a shot over the bar as the hosts continued to press, but Stanley replied when Paul Mullin teed up Ian Craney, only for him to place a shot inches wide.
Roscoe D'Sane ought to have done better for Stanley when he volleyed wide from just 12 yards, and then Jay Harris saw a powerful drive saved by Conrad Logan.
Liam Dickinson was next to go close for Stockport on 26 minutes. He ran purposefully at the Accrington defence before shooting just over from 20 yards. Rose then hit a daisy-cutter wide from all of 35 yards.
This was a cracking game though, and D'Sane twisted and turned before shooting straight at Logan.
However, Stockport went on to double their lead in first-half stoppage time when Elding rose well to head home Rose's in-swinging corner kick.
Mark King blasted well over for Stanley after the restart, before Stockport youngster Leon McSweeney saw his shot deflected into Ian Dunbavin's hands after a jinking run across the edge of the box.
Craney blasted a disappointing shot way over the bar for the visitors, before substitute Shaun Whalley did likewise with 12 minutes to go.