Dartford became 13th visiting side to win at Edgeley Park in the Blue Square Premier this season, leaving the Hatters precariously close to relegation to the Blue Square North.
The visitors settled into the game quickly, the large crowd inside Edgeley Park appearing to spur them on. Richard Rose with an early effort over the bar after James Tunnicliffe's clearance was charged down, Charlie Sheringham seeing a header saved comfortably by Richard O'Donnell moments later.
County's first effort coming after neat play from Lee Bullock who found Mark Cullen in space, Tom Bonner clearing the danger.
The Hatters gradually started to make their mark on the half, Keiran Charnock's header saved by Csaba Somogyi, a deep cross from Sam Sheridan, after good work by Jordan Fagbola, also saved by Somogyi under pressure from Alex Kenyon.
County earned the first corner of the game, as Jon Nolan's shot was deflected wide after a superb pass from Sheridan to Cullen who in turn found Nolan.
The visitors were dangerous on the counter attack and only a great tackle from Fagbola cleared the danger after Sheridan's misplaced pass had put the Hatters defence under pressure.
The Hatters suffered a blow when the recalled Charnock had to be substituted with a recurrence of his thigh injury, Danny Whitehead coming on with Sheridan reverting to right back.
Sheridan was in the action immediately to clear the ball off Jack Evans' toes after he had found space in the box.
Sheringham then missed the chance of the half as he stood on the ball in front of an open goal after Nathan Collier took advantage of a mix up between Sheridan and Fagbola to find the striker free in the box.
HT: Stockport County 0 Dartford 0
The Darts almost opened the scoring in the opening minutes of the second half as Richard O'Donnell was forced into action, making a brilliant save to deny Sheringham after Tunnicliffe's miss kick had put the striker through on goal.
The Hatters keeper was tested on several occasions as the visitors took control of the game, tipping a 25 yard effort from Evans over the bar, Lee Bullock heading clear from the resulting corner kick.
The Hatters best chance of the half came the way of Kenyon after good work from Macken and Whitehead, Somogyi making a comfortable save.
Collier missed a chance as his effort clipped the bar before the visitors finally got the goal their efforts deserved, Sheringham heading home from Hayes' cross after Nolan had lost possession in midfield. Nolan being substituted for Paul Marshall soon after.
Marshall saw his first effort on goal deflected onto the bar by Bonner after good play from Newton had found him in the box.
Somogyi, rarely troubled throughout, claimed a couple of crosses to ease the pressure on his defence, before Hayes missed a chance to put the game to bed late on, curling his left foot shot wide after Sheridan had given away possession in the middle of the park.
FT: Stockport County 0 Dartford 1
Starting XI: O'Donnell, Newton, Tunnicliffe, Kenyon, Sheridan, Cullen (Mainwaring), Nolan (Marshall), Fagbola, Macken, Charnock (Whitehead), Bullock.
Subs: Ormson, Whitehead, Brownhill, Mainwaring, Marshall.
ATT: 6,113 (135)