Adam Griffin's drilled effort on the stroke of half-time proved enough to fire Stockport to a seventh successive league win at Accrington's expense.
The midfielder thumped home Anthony Pilkington's cross for his third goal of the season, but County failed to add to that despite their dominance.
Goalkeeper Przemyslaw Kazimierczak was the hero for the hosts, in particular with two superb saves from Pilkington.
Robbie Williams had Stanley's best effort, but was off-target from range.
Accrington: Kazimierczak, Richardson (Whalley 46), Williams, Edwards, Almeida, Rogers, Boco, Harris, Grant (Proctor 76), Fleetwood (Todd 46), Mullin.
Subs Not Used: Welch, Doherty.
Stockport: Hennessey, Clare, Williams, Owen, Rose, Poole (Bramble 76), Taylor, Blizzard, Griffin, Elding (Dickinson 88), Pilkington.
Subs Not Used: Spencer, Dinning, Rowe.
Booked: Clare, Elding.
Goals: Griffin 45.
Att: 3,004
Referee: R Lewis (Shropshire).