Teenage striker Michael Smith led the line superbly at Moss Rose on Saturday, scoring the killer goal in the 79th minute of the League Two encounter when he converted a Mark Convery cross with a bullet header at the far post.
Earlier in the eighth minute, the Quakers had taken the lead when centre-back Ian Miller powered home another Convery cross with a header in off the crossbar.
In between, Darlington could have added further goals, with Michael Smith twice denied by keeper John Brain and John McReady lofting a simple chance over the bar. Convery, however, wasted their best chance to extend their lead when his 53rd-minute penalty was well saved by Brain after Paul Bolland was judged to have brought down substitute Nathan Mulligan.
The hosts too had their chances, with Nathaniel Brown heading wide after 38 minutes before seeing a firm volley blocked in the six-yard box on the stroke of half-time.
But their best chance to equalise fell to Emile Sinclair, who poked wide from 12 yards with only the keeper to beat after a neat header from Matthew Tipton had put him in the clear.