Wrexham's poor home form struck again as a series of chances went begging, while Stockport were content to pick up points.
Home manager Denis Smith admitted it was frustrating to be up against a dramatically changed Stockport side.
He said: "They have a new manager and he has brought in experience. He has changed the team and it is paying off.
"They are going to be a hard side to beat from now until the end of the season." Smith believes an early goal would have helped his men to settle and they might have had more luck when they hit the crossbar and saw efforts saved.
Stockport manager Sammy McIlroy said that he wanted more consistency from some of his players, but he praised County's travelling supporters for getting behind the team He added: "We knew it would be tough here against a big strong side.
"I know the home fans were booing at the end, but I would love to be in Wrexham's situation now. The crowd could boo me all day." Chris Armstrong saw an early shot tipped over the bar by Anthony Williams, Steve Thomas fired a high shot into the crowd and Dennis Lawrence headed just over from a corner.
That was the nearest the Red Dragons came to scoring in a dull first half, while at the other end defender Steve Roberts had to make a great tackle to deny Fraser McLachlan on the edge of the box and a free-kick from Danny Griffin hit a Wrexham post, before goalkeeper Andy Dibble turned the rebound away for a corner.
Just before half time Dibble made a good block to stop Aaron Wilbraham, after the striker had rounded Brian Carey and was about to shoot from close range.
Wrexham improved in the second half but Chris Llewellyn, Stephen Thomas, Lawrence and Carlos Edwards missed good openings by shooting straight at the keeper.
Late substitute Hector Sam had a shot saved and Jim Whitley was out of luck with a 30-yard drive that crashed against the County cross bar.
County had a penalty appeal rejected when Wilbraham went down under a Lawrence tackle in the box.
As the match fizzled out in a goalless draw, some sections of the home crowd booed the players to show their disappointment with the home form in sharp contrast to the excellent displays that Smith's men provide away from the Racecourse.