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Two goals in four minutes by Danny Harris and Luke Wilkinson earned Dartford their 10th Blue Square Bet South away win of the season at Hayes Lane on Monday.
Michael Malcolm's 30-yard free-kick pulled one back for relegation-threatened Bromley with 13 minutes left, when the ball crept under Louis Wells, but the Dartford goalkeeper responded well by pulling off a fine save to keep out Ali Fuseini's late effort.
Tom Champion headed Lee Noble's corner wide, before Harris (pictured) fired them in front with his 18th goal of the season after 22 minutes when he seized on a defensive mistake to beat Ebbsfleet loanee Joe Welch.
Noble was also the provider for the second when another set-piece found an unmarked Wilkinson who continued his impressive scoring record, heading in his fourth goal since arriving on-loan from Dagenham & Redbridge in late February.
Skipper Elliot Bradbrook went close twice in the second half, before Malcolm gave Bromley hope when his effort bounced in front of Wells and went in.
Wells' fine stop from Fuseini kept Darts in front, but Woking's two Easter wins still leaves them seven points behind the leaders with three games left.