Wrexham fell to their second defeat of the campaign as Paul Mullin's early opener wasn't enough for three points.
Mullin scored after just two minutes, before Paddy Madden's header levelled just after the break and Ryan Rydal scored the winner with ten to play.
Phil Parkinson stayed with the same starting XI as that beat Dagenham a week previous but Devonte Redmond and Bryce Hosannah took a place on the bench in place of Dan Jarvis and David Jones.
The game began is perfect fashion for Wrexham as they took the lead with less than two minutes played. Rob Lainton picked up the ball and drove it down the pitch for Mullin to latch on to, dinking the goalkeeper and sending the 1,700 Wrexham fans wild in the away end.
Wrexham almost doubled their advantage on 13 minutes as Liam McAlinden turned and drove forward before hitting a shot destined for the bottom left corner from 30-yards out, but the goalkeeper got a vital touch.
Stockport's best chance of the first half fell to Madden who got on the end of a sloppy pass from Wrexham and forced Harry Lennon to make a superb block to deny.
Seconds later Mullin had a shot of his own intercepted in the box before Lennon's long ball was headed goalbound by Mullin only to be denied by the goalkeeper.
The first half was dominated by Wrexham with the hosts rarely threatening and Parkinson was certainly the happier of the two managers going into the break.
Half-Time: Stockport County 0-1 Wrexham
If Wrexham had dominated the first half, then County had bossed the second. Within three minutes of the re-start they were back on level terms.
A corner was swung in and Madden met it with his head to thump the ball into the back of Lainton's net.
Wrexham almost responded immeditely as McAlinden played in Mullin who had a shot blocked once more.
As the half went on Wrexham looked ropey, with mistakes becoming more freequent as the minutes rolled on. County confidence continued to grow.
Wrexham's best chance of the half came on 75 minutes as Young's corner was met by a Ben Tozer volley - but it went just wide.
With ten minutes to play a mistake from Wrexham in the middle led to a Stockport break, and after some chaos in the box it was put home by Rydal.
Wrexham were unable to get back into the game and as such fell to defeat for the second time this campaign.
Wrexham Line-Up: Lainton, French, Tozer, Hayden, Lennon, Reckord, Young, J.Jones, McAlinden (Redmond, 78), Ponticelli (Angus, 73), Mullin
Unused Subs: Dibble, Hosannah, Cleworth
Stockport Line-Up: Ross; Barclay (Hogan, 42), Palmer, Fryers; Southam-Hales, Rooney, Croasdale, Kitching (Rydel, 78); Reid (Collar, 86), Madden, Whitfield.
Unused Subs: Hinchliffe, Fish.
Attendance: 7,771 (1,700 away)
Man of the Match: Paul Mullin