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Tom Champion’s injury-time winner booked Dartford a place in round two of the FA Trophy.
The first-half substitute volleyed home in the second minute of stoppage time to dump Blue Square Bet Premier side Crawley Town out of the competition.
Crawley, who caused an upset in the FA Cup this season after beating League 1 Swindon, found themselves on the receiving end of a cup shock at Princes Park.
The two teams had already fought out a 3-3 draw at Crawley on Saturday - a game which saw the Darts leading 3-1 until the hosts scored two late goals to take the tie to a replay.
Champion had missed out on the original tie as he had work commitments in America but flew back in time to inflict defeat on Steve Evans’ non-league high-flyers.
Tony Burman’s (pictured) Dartford side will now meet Ashford Town (Middlesex) in the last 32.
The Darts were on the back-foot early on in the tie, and survived a first-minute penalty scare when Sergio Torres went down in the box, as Crawley came surging forward but the defence held out.
Andrew Young also did well to tip Torres’ long-range effort over the bar.
Torres was at the centre of everything and the Darts had their own penalty shouts turned down as they felt the Crawley man handled in the box.
Michael Shinn headed an effort off the line but the Darts held out until the break with Champion coming on late in the half during a tactical re-shuffle.
Young made another good save in the second half, this time from his own player, as Lee Burns accidentally sent an effort in on his own goal.
With extra-time looming Elliot Bradbrook, who was also in America when the first clash took place, sent in a corner and after keeper Michel Kuipers had palmed it away Champion, from the edge of the box, smashed home to win the tie.