Gareth Evans grabbed a goal in each half as Macclesfield clinched victory.
The 20-year-old forward opened the scoring, latching on to a neat ball from Emile Sinclair before firing a left-footed volley into the far corner.
Darlington did pull level on the hour mark when visiting keeper Jon Brain got in a muddle with a team-mate Hessey and David Poole shot home from 12 yards.
But Evans netted the winner from the penalty spot after a foul on Emile Sinclair by Clayton Fortune.
Darlington: Oakes, Valentine, Miller, Foster, Ryan (Fortune 55), Poole, Barnes (Main 46), Kennedy, Hulbert, Griffin (Gray 70), Carlton.Subs Not Used: Kazimierczak, White.
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