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Dartford's relegation plight worsened when they lost at home to fellow strugglers Chester on Friday night.
There were 1,610 fans inside Princes Park and many more watching at home, with the game screened live by BT Sport.
But they endured a poor spectacle which was settled by a rare piece of quality from Gareth Seddon, six minutes into the second half.
Defeat leaves the Darts four points from safety and with all the other sides around them still to play on Satuday afternoon.
Dartford welcomed back Tyrone Sterling, the left-back having missed Saturday's game at Southport with a hamstring injury. Centre-half Mat Mitchel-King, who was forced out of that game early with an ankle knock, was also fit enough to start.
A wretched first half passed almost without incident.
Both sets of fans generated a good atmosphere from the start and Dartford went close in the opening few minutes when on-loan Luton striker Alex Wall rolled the ball across the face of goal.
The home side had a good tempo about their play, without much to show for it in the final third. Jim Stevenson floated a cross-shot just over the bar but it could barely be classed as an attempt on goal.
Chester looked to play on the counter-attack, no doubt under instruction from manager Steve Burr to tighten up defensively having conceded six goals in their previous two games.
A couple of crosses, easily gathered by Dartford keeper Alan Julian, were the sum total of Chester's efforts in the first 45 minutes.
But the visitors looked brighter after the restart. John Rooney's perfectly-weighted through-ball sent Matty Taylor running into the box but Julian was alert to the danger, diving at his feet to save.
Moments later, a pass from Nathan Turner bisected two Darts defenders and Lewis Turner swung in a cross from the byline. It skipped off a Darts head and fell to Seddon, who headed wastefully over from close-range.
Seddon had his head in his hands but he was soon spreading them in celebration. Chester worked the ball down their right-hand side and Seddon volleyed the bouncing ball across Julian into the far corner from just inside the box.
Dartford, energetic in the first half, had fallen flat. The visitors were suddenly first to the loose balls and Taylor went close with a left-footed shot which scudded past the base of the post.
At the other end, Wall burst into the box in pursuit in pursuit of a flick-on. He challenged for the ball with goalkeeper Aaron Chapman and went to ground, but referee Kevin Johnson waved away Dartford's penalty appeals.
Change was needed and it came in the form of Lee Noble, who replaced Alex Woodyard. Noble had Dartford's first shot on target moments after coming on but Chapman made a straightforward save down to his right.
A slack pass from Taylor was then snaffled by Noble, whose diagonal pass sent Harris racing towards the box. He tangled with a defender but the shouts for a foul were louder off the pitch than on it.
Darts boss Tony Burman threw on Mikel Suarez as a second target man alongside Wall. But as the home side pushed men forward, gaps started to appear at the back and Rooney drilled a shot wide for Chester.
Seddon climbed well to meet a left-wing cross although his header flashed wide of the far post.
A left-wing corner from Noble curled onto the head of Bradbrook but he couldn't keep his effort down and Chester survived.
Noble arrowed a powerful shot towards the bottom corner as Chester dropped deeper into defence, but Chapman made a fine save to push the ball behind.
The only piece of link-up play between Suarez and Wall saw Suarez flick on a high ball forward, only for Wall to trickle a tame shot into Chapman's gloves.
Chester's sizeable travelling contingent celebrated noisily at full-time, knowing they'd delivered a potential knockout blow to one of their rivals for survival.
Dartford: Julian, Burns, Mitchel-King, McAuley, Sterling, Woodyard (Noble 63mins), Cornhill (Suarez 74mins), Stevenson (Collier 82mins), Bradbrook, Harris, Wall. Subs not used: Clark, Ibrahim.
Chester: Chapman, L Turner, Linwood, Killock, Heath, Mahon (Lindfield 90mins), N Turner, Bond, Rooney, Taylor (Daniels 90mins), Seddon. Subs not used: Danby, Bridge, Menagh.
Attendance: 1,610.