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Charlie Sheringham scored the fourth goal of his Dartford loan spell to increase Stockport’s relegation worries on Saturday.
A bumper crowd of 6,113 turned up at Edgeley Park but the Darts, playing their fourth game in eight days, defended well and restricted the hosts to limited chances.
James Tunnicliffe’s header was saved by on-loan goalkeeper Csaba Somogyi and Jon Nolan fired wide before Somogyi denied Lee Bullock.
At the other end, Jack Evans and Sheringham both drew good saves from County No.1 Richard O’Donnell.
The winner arrived 18 minutes from time, Ryan Hayes crossing and Sheringham, right, heading home.
Dartford withstood late Stockport pressure, with Tom Bonner deflecting an effort from former Manchester City striker Jon Macken onto the bar.
The win leaves the Darts eighth in Blue Square Bet Premier with two games to play. They visit Forest Green Rovers on Tuesday before finishing the season at home to Nuneaton Town on Saturday.