An 80th minute winner by sub Nathan Cartman gave Quakers the points in a thriller at Broadhurst park.
Quakers led 2-0 at one stage, but FC United came roaring back.
But Quakers kept calm, and sub Nathan cartman struck the winner.
Quakers got the game’s first corner on 3 minutes. Josh Gillies whipped the ball in and keeper Ashley Frith palmed the ball away.
Quakers took the lead on 4 minutes, when Liam Hardy latched on to a long ball by Stephen Thompson, ran into the area, and slipped the ball past the advancing Ashley Frith.
Quakers nearly got a second when Josh Gillies got to the bye line, and pulled the ball back into the six yard box, where Frith fumbled it but held on at the second attempt.
There was a scare for Quakers when Nathan Lowe got around the back of the defence with Peter Jameson out of his goal, but Phil Turnbull headed the danger away.
It was nearly 2-0 when Terry Galbraith made a good run downfield and squared for Leon Scott, whose left foot shot went just past the post.
Frith then made a hash of a clearance, hitting the ball against Hardy, but Quakers couldn’t take advantage when the ball ran loose.
Stephen Thompson then made a fantastic run from inside his own half to well inside the United penalty area and fired towards the bottom corner, but Frith just managed to get a hand to the ball and prevent a goal.
Another chance came Quakers way on 24 minutes, when a spell of pressure ended when Gary Brown headed a delicate right wing cross by Thompson just wide.
Quakers deservedly went 2-0 up on 27 minutes. Liam Marrs free kick was headed down by Mark Beck for Hardy to lay off for Thompson to fire across Frith into the net.
United pulled a a goal back on 42 minutes out of the blue, when Jason Gilchrist picked the ball up on the right 30 yards out, spotted Jameson off his line, and chipped the ball neatly over him to give his team a much needed lift.
But Quakers nearly scored immediately. Brown’s long throw was cleared as far as Thompson, who hit a low left foot shot that whizzed just past the post.
FC United 1 Darlington 2
In the first minute of the second half after Adam Mitchell came on for Gillies, Quakers had a chance when Thompson played a 1-2 with Hardy, and fired just wide.
Hardy was denied the third by the woodwork, when Brown crossed perfectly from the for Hardy to beat Frith, but the ball came back off the crossbar.
Another chance fell to Thompson on 50 minutes just inside the box, but Frith fingertipped his effort over the top.
Hardy fired across the face of goal, and Thompson had a shot blocked by Frith as the opportunities kept dropping to Quakers.
But with the crowd behind them, United built up a head of steam, and George Thomson headed straight at Jameson from a right wing cross.
And united broke through on 66 minutes, when Thomson ran at the defence, and beat Jameson with a low shot.
But Quakers came back and nearly scored, when Thompson chipped a free kick into the area, and Burgess was inches wide with a header.
Another chance went begging on 75 minutes, when Beck flicked the ball on for sub Nathan Cartman, who beat Frith, but the ball slipped just past the post.
But at the other end, Chris Chantler hit a low shot that Brown hooked off the line.
But Quakers broke away and went 3-2 up with ten minutes left. Cartman cleverly found Purewal with an overhead kick for Purewal to go up the left. His ball to the far post was blocked, but it came back out to C|artman, who struck a low shot that took a deflection and looped over Frith.
And it was nearly 4-2 when Beck sent Cartman racing clear, but the keeper blocked his shot at the near post.
But Jameson still had to be alert to block Dale Johnson at point blank range.
Jameson, Marrs , Galbraith, Turnbull, Burgess, Brown, Thompson, Scott, Beck, Hardy, Gillies
Subs: Cartman, Bell, Mitchell, Nowakowski, Purewal
Frith, Tonge, Chantler, Kay, Eckersley, Ashworth, Glynn, Lowe, Greaves, Thomson, Gilchrist
Subs: Winter, Johnson, Wolfenden, Williams, Sheridan