Quakers were agonisingly beaten by a last minute goal from Harrogate.
Reece Styche, on his debut, had put Quakers back into the game with an equaliser eight minutes from the end, but Harrogate won the game from a last minute corner.
Quakers started brightly and won the first corner in the second minute and the ball dropped for Styche who couldn’t quite turn it, and Harrogate cleared.
Then David Syers won the ball in midfield and tried to set Styche away, but Harrogate keeper James Belshaw got to the ball first.
Harrogate had a free kick on the right on 12 minutes awarded fro a foul by Gary Brown, but Leesley’s inswinging free kick was headed away.
Stephen Thompson then had a good run down the right on 14 minutes that took him into the box, but Belshaw held on to his low cross.
Quakers had their first shot at goal on 22 minutes when Thompson slipped the ball to Luke Trotman on the corner of the box, but the full back fired well over the bar, and on the half hour Terry Galbraith headed a Phil Turnbull free kick into the keeper’s hands.
Greg Mills then made a good run up the left against two defenders and crossed well from the bye line, but another defender headed the ball away on the six yard line.
Harrogate were forced into a change on 38 minutes when Terry Kennedy limped off and was replaced by Lachlan Barr.
Tom Portas then made a good interception at the other end when Leesley broke down the left and crossed into the middle for George Thomson, but Portas got back and took the ball off his feet.
Half time 0-0
Goal! 1-0. Quakers took the lead on 49 minutes. Mills was brought down as he tried to win the ball inside the Harrogate box afetr Styche headed the ball on, and the ref pointed to the spot from where Styche coolly tucked the ball away.
Goal: 1-1 But Harrogate were level six minutes later. Jordan Thewlis broke into the box and was brought down by keeper Ed Wilczynski, and Leesley cracked in the penalty.
Goal 1-2 Harrogate went ahead on 58 minutes when Lachlan Barr headed in a right wing cross by Leesley.
Quakers nearly levelled with a superb volley by Greg Mills from a Thompson cross that Belshaw parried but Styche couldn’t quite force in the rebound.
Thompson also had a shooting chance on 75 minutes when he found space 25 yards out, but he fired straight at Belshaw, then Brown fired over the top after his long throw had come back to him.
Goal: 2-2! Quakers got back into it on 82 minutes when a headed clearance found Styche on the left, and the striker charged into the box, leaving a defender in his wake, and at full stretch he steered the ball into the net past Belshaw.
But just as a Tuesday replay was on the cards, regained the lead deep inside the last minute when Leesley headed in a Thomson corner at the near post.
Darlington 2 Harrogate Town 3
Wilczynski, Galbraith, Collins, Brown; Trotman, Mills (sub Gillies 80); Turnbull, Portas (sub Saunders 79), Syers, Thompson (sub Caton 81); Styche
Subs: Vaulks, Bancroft,
Belshaw, Vann, Swain, Falkingham, Kennedy (sub Barr 38), Burrell, Thomson, Agnew, Mulhern (sub Hudson 79), Thewlis, Leesley
Subs: Cracknell, Gooda, O’Hanlon