David Syers popped up with the winner just three minutes from the end to give Quakers three valuable points and lift them eight points clear of the relegation zone.
Syers scored his seventh of the season from a great free kick from Josh Gillies that gave Quakers their third straight home win and also celebrate the opening of the new seated stand.
Curzon had the first chance on 3 minutes when the ball came in from the right and Ben McKenna missed his kick from six yards out.
But Quakers went down the other end and nearly scored, when David Syers played the ball inside to Reece Styche, who fired inches over the top from the edge of the box.
However, Curzon nearly scored with a header by Daniel Shaw from a corner that Ben O’Hanlon headed off the line.
The play swung from to end, and Styche had another opening on the edge of the box, this time a left foot shot that Mason saved at full stretch to his left.
Curzon nearly took the lead on 20 minutes when a good cross came in from the left from Sam Walker to Jake Dunwoody, who caught the ball full on the volley and forced a great save out of Aynsley Pears.
Quakers had a penalty appeal turned down when James Caton chased a chip forward by O’Hanlon into the box and went down when challenged, but the ref waved the appeals away.
Curzon had another chance when Wharton set up Guest twelve yards out, but the full back fired straight at Pears.
Quakers won their second corner on 35 minutes, teenager Mitchell Glover, making his full debut, curled the ball from the Darlo left into the six yard box, and Heaton was penalised for a foul on the keeper as the bal lwent into the net.
Quakers nearly took the lead on 42 minutes, when Glover found Caton on the corner of the box, and Caton curled the ball into the near post where Mason just managed to palm the ball away.
Half time 0-0
Quakers made a sub at half time, Josh Gillies coming on for James Caton.
Curzon had a chance on the break when Rowney found James Baillie on an overlap on the right, and the full back fired into the side netting.
But Quakers replied when a left wing corner by Gillies dropped to Thompson at the far post, and his volley was blocked a couple of yards out.
Quakers were awarded a penalty on 55 minutes when Styche got around the back of the defence and set up Syers whose shot was blocked by Mason, and as Gillies went for the loose ball, he was brought down by Mason. The ref pointed to the spot, but Thompson’s spot kick was blocked by the keeper.
Quakers missed a great chance on 59 minutes when Thompson got round the back of the defence on the right and set up Styche, whose shot was blocked and the ball ran for Gillies who sidefooted wide.
Quakers made their second sub on 75 minutes when Glover, who had a useful debut, was replaced by Greg Mills.
Quakers had more of the possession at this point, but Curzon had a chance on 77 minutes when Walker got through on the left, and fired towards the opposite corner, but Pears fingertipped the ball wide.
However, Quakers nearly won it when Mills won the ball in midfield, ran forward, and hit a low left foot shot that Mason just managed to touch around the post.
But Quakers won the game with three minutes left. Thompson was fouled on the left, Gillies curled the free kick in beautifully for Syers to head powerfully past Mason, his seventh of the season.
Darlington: Pears, Trotman, O’Hanlon, Turnbull, Heaton, Galbraith, Caton (sub Gillies 46), Glover (sub Mills 75), Styche, Syers, Thompson (sub Scott 90+2)
Subs Bancroft, Vaulks,
Bookings: O’Hanlon, Styche
Curzon Ashton: Mason, Baillie, Guest, Hunt, Shaw, Regan (sub Dwyer 81), Rowney (sub McKenzie 86) , Walker, Wharton (Brooke 71), Dunwoody, McKenna
Subs: Clark, Thornley