Two Danny Lloyd goals, the second from the penalty spot, and a Jimmy Ball header kept Stockport in the Conference North promotion hunt
County started the day fifth, visitors Stalybridge in the relegation places in 21st. The home side dominated the opening proceedings, restricting Celtic to a series of corners and long shots.
And they took the lead after eight minutes, Lloyd poking a Josh Amis flick-on past Celtic keeper Grant Shenton.
County, finding most success down the flanks through man-of-the-match Sam Minihan and Scott Duxbury, almost doubled their lead after 20 minutes but Amis shot over after a neat turn in the box.
Minutes earlier Lloyd had played in John Marsden but the ball rolled through to Shenton.
On 36 minutes a curling cross by Lloyd from the right was just a fraction away from the head of a diving Amis.
The visitors’ best chance of the half arrived on 42 minutes when Dunbar shot across the County goal.
Stalybridge levelled a minute after the restart, Dunbar curling his shot high into the net after some ponderous County defending.
Elliott Osborne then crossed in low but Chris Smalley couldn’t quite stretch far enough at the far post.
The home fans wanted a red card when Matthew Hughes fouled Lloyd on the edge of the box as he bustled through but covering defenders meant the visiting captain was only booked.
Stalybridge had a great chance with 20 minutes to go, Dunbar firing just wide from 12 yards, Lloyd then doing the same up the other end.
On 73 minutes, Lloyd added his second from the penalty spot after he was pushed over in the box by Daniel Wilkins.
And with a couple of minutes on the clock, sub Ball headed in a corner to wrap up the points.
County: Ormison, Minihan, Duxbury, Montrose, Clarke, Smalley, Osbourne, Meppen-Walters (Ball 58), Amis, Marsden (Felix 66), Lloyd (Ross 84). Subs: Ross, Smith, Odejayi
Man of the Match: Minihan