A superb goal from Ricky Lambert - his fourth in five games - was the difference between the two sides on a blustery afternoon at Edgeley Park.
Lambert's first-half strike was just the ticket for County boss Sammy McIlroy, whose side are now looking a much better bet for survival after securing ten points from their last four games.
Struggling Stockport welcomed a bumper crowd and both sets of fans had much to shout about early on.
Wednesday started brightly enough and after Graeme Lee had gone close with a shot from distance, Adam Proudlock rose highest in the box to glance a header on to the crossbar.
However, County were celebrating on 24 minutes when Lambert drove a shot into the top corner of Kevin Pressman's goal from all of 25 yards.
Jon Daly almost doubled the lead on 35 minutes, but his shot flew inches over.
The home side kept up the momentum after the break with Northern Ireland international Danny Griffin and youngster Ashley Williams both threatening the Wednesday goal.
The best Wednesday could muster was a double effort from Lewis McMahon following a flurry of corners.
Delighted Stockport boss McIlroy said: "Once we got settled down we created a few chances and scored a fantastic goal.
"If Ricky's goal had been scored in the Premiership, we would have been seeing it again and again every Saturday.
"Our workrate was first-class, it was a great battling performance.
"We have had a bit of luck lately, but we've had to fight and ride that luck.
"There have been games early in the season when we've come off the pitch hardly believing we've lost. I am pleased for all the players, I'm proud of every one of them."