Harrogate Town were held to a point at Edgeley Park after Jason Oswell's second half brace cancelled out Simon Ainge's first half strikes.Two goals in the space of five minutes from AInge, including a memorable volleyed first, put Town firmly in command at the interval, though County would come back strong.
Oswell struck eight minutes after the restart with a clever near post finish, before pouncing to turn Sam Minihan's parried shot into an empty net.
Both sides made one change from their respective Tuesday night wins as Dom Knowles replaced Jordan Thewlis for Town, while Sam Walker replaced Stephenson for the hosts.
After George Thomson and Jimmy Ball had exchanged shots, the first chance of the afternoon fell to Matty Warburton six yards out, but Ben Middleton made the block.
Jack Emmett then went close to creating the opener as his drilled cross was turned goal wards by Ainge, but scrambled away a fraction before crossing the line.
With 24 minutes gone, Ainge produced an early contender for goal of the season as he met Leesley's cross field ball with a first time volley that flew past Ben Hinchliffe.
Ainge doubled his tally five minutes later as Ben Parker sent a deep cross to the back post that Ainge guided into the far corner with his head.
County boss Jim Gannon then felt the need to make a change, and introduced Ben Mckenna in place of Walker to try and alter the course of the contest.
The hosts looked more assured as the half ended, and found a way back into the contest eight minutes into the second half as Oswell was first to Sam Minihan's cross and converted at the near post.
Oswell's finish handed the momentum to County, and it could have been level had a blue shirt got on the end of Connor Hampson's teasing cross before Town could clear.
The hosts had looked an entirely different outfit since finding the net, and pulled level after 71 minutes when Oswell was first to react to James Belshaw keeping out Minihan's shot and slid into an empty net.
Warren Burrell almost put Town back into the lead with ten minutes left toplay, but fired over after turning sharply in the box.
Ryan Fallowfield then came close to providing a winner, but saw Hinchliffe beat away his near post effort as Town were made to settle for a draw.
Harrogate Town: Belshaw, Fallowfield, Parker, Falkingham, Middleton, Burrell, Thomson, Emmett, Ainge, Knowles, Leesley (Vann 71)
Subs not used: Lees, Cracknell, Kennedy, Day
Goals: Ainge 24, 29
Booked: Thomson, Middleton, Vann
Stockport County: Hinchliffe, Cowan, Hampson (Duxbury 84), Winter, Clark, Smalley, Minihan, Ball, Oswell, Warburton (West 92), Walker (McKenna 35)
Subs not used: Smith, Brazel
Goals: Oswell 53, 72
Referee: S Copeland