The Pilgrims led 1-0 and 3-1 - but Darlington were back on terms at 3-3 by the 68th minute. Two quickfire goals from Jack Waddington and Owen Sheriff sealed Boston's victory.
United's first half goals had come courtesy of Han Stevens and a brace from Oskar Rajski.
Boston (3-4-2-1): Jake Lovelace; Oskar Rajski, Owen Sheriff, Taylor Jaine; JJ Ward (Patrik Bad 85), Jake Henderson, Rueben Fogg, Josh Doran (Lucas Stubbs 73); Han Stevens, Kyle Featherstone (Jack Waddington 65); Flynn Slater (Jake Higginbottom 77).
Referee: Istvan Mod.
PIC: Steve Davies.