Quakers were beaten by three second half goals at Wetherby Road, after holding their own in the first half.
Harroagte jtook control of the game in the first minute of the second half, although Quakers never stopped battling.
Darlington defender Gary Brown was booked for a late challenge on Jack Emmett in the second minute
Harrogate had a couple of free kicks from wide positions which the Darlo defence dealt with.
Quakers had their first attempt at goal on 8 minutes, a long range effort by Reece Styche that went a few yards wide.
Darlington midfielder Joe Wheatley became the second Darlo player to be booked for a foul on Josh Falkingham on 14 minutes.
Harrogate then had a chance with a header by Mark Beck that went wide, then Leon Scott made great block ten yards out to stop an effort by Emmett.
Quakers had a free kick from just inside their own half on 28 minutes that was taken by Turnbull and found Heaton inside the Harrogate box, but his header went straight to Belshaw.
Quakers got a free kick for a foul on Gillies on 36 minutes, but Wheatley fired the free kick into the wall.
At the other end Leesley had his free kick blocked, and then fired the rebound well over the top.
Quakers had their first effort on target on 41 minutes. Thompson was challenged outside the box and the ball ran for Wheatley, who took a touch and hit a swerving right foot shot that Belshaw pushed away.
Just on half time, Heaton got back very quickly to get the ball out for a corner when Thewlis broke into the box.
Quakers nearly took the lead in stoppage time. Thompson chested the ball down for Syers, who hit a powerful shot from 25 yards that Belshaw pushed over the top.
Half time 0-0
Quakers went a goal down within a minute of the restart, Warren Burrell made a great run down the right, got past Leon Scott, and set up Emmett, who drove the ball into the roof of the net from 12 yards.
Harrogate went 2-0 up on 54 minute. Josh Gillies shot was charged down in the Harrogate box and the ball rebounded out to Thewlis, who ran through one-on-one only for Talbot to block well. However, Leesley kept the ball alive and set up Thewlis who fired past Talbot.
Stephen Thompson replied with a shot from the edge of the box that went straight at Belshaw.
Quakers made two subs, Scott and Turnbull coming off for Saunders and Galbraith
Saunders had a chance from 12 yards out, but he blazed over the bar, and a few moments later he seemed to be pulled back in the box when he chased a through ball, but the referee waved play on.
Darlo then made a third sub on 68 minutes, Mills coming on for Gillies.
But Harrogate had a chance for 3-0 on 76 minutes when Emmett got away down the right with just Talbot to beat, but he fired across the face of goal.
Quakers nearly got a consolation in stoppage time when Thompson drove the ball low into the box for Styche, at full stretch, to turn into Belshaw’s hands.
But it was 3-0 in the last minute when Leesley dribbled past three defenders and lashed the ball past Talbot.
Talbot, Collins, Heaton, Brown, Scott (sub Galbraith 55), Gillies (sub Mills 69), Turnbull (sub Saunders 55), Wheatley, Thompson, Styche, Syers
Booking: Brown, Wheatley, Galbraith, Thompson
Belshaw, Swain, Parker, Kennedy,Burrell, Falkingham, Agnew, Emmett, Beck, Thewlis, Leesley
Subs: Thompson, Cracknell, Lees, O’Hanlon, Knowles