Within two minutes of the start, Michael Woods set up Ashley Worsfold who flicked his shot just over the bar.
County settled better and the Town defence had to deal with a series of crosses and corners.
Aman Verma wasted a chance to give County the lead when a Rhys Turner header found him unmarked, but he contrived to screw his shot well wide.
Woods,making his first full start, chipped over the defence for Worsfold who crashed his drive against the upright.
As half time approached,a three goal burst in under four minutes shell shocked Stockport.
There seemed little danger as Adam Bolder advanced through the middle, but he suddenly unleashed a 25 yard drive into the bottom corner which comprehensively beat Ian Ormson.
The cheers had hardly subsided, before Woods half volleyed a wayward defensive header into the roof of the net to make it two.
Two minutes later a powerful run by Woods was halted on the edge of the area,but the ball broke loose to Chris Hall who made no mistake from close range.
Stockport had plenty of second half possession as they tried to hit back.
Adriano Moke soon made an opening for Verma, but he couldn’t generate enough power to beat Craig MacGillivray.
On the hour,Moke’s free kick was headed over by Verma before at the other end, Woods rounded Ormson only to see, Jordan Fagbola clear off the line.
County applied late pressure as Town took their foot off the gas.
Substitute,Iain Howard headed over from Turner’s centre, before James Tunnicliffe forced an excellent diving save from MacGillivray.
With three minutes left,Howard pulled one back when he brought down a Kyle Jacobs cross and shot past MacGillivray.
The match had an unfortunate postscript when Stockport manager, Ian Bogie, resigned from his position.
Town. 1 MacGillivray, 2 Bloomer, 3 Merris,4 Bolder ( Rowe 66 min), 5 Franks, 6 Killock (c), 7 Worsfold ( Hardy 79), 8 Brown, 9 Hall ( Wright 79), 10 Woods, 11 Nelthorpe.
Unused subs 15 Nowakowski, 16 Samuels.
Scores Bolder 38, Woods 39, Hall 42 mins. Bookings nil Att.918