The Pilgrims led 2-0 inside the first 15 minutes at RAF College Cranwell — but were pegged back with goals either side of half-time.
Bradley Easey and Louis Saebe scored United’s goals to extend their own unbeaten league run to six matches — and become the first side in 11 matches to stop the Nottingham-based opponents winning.
Boston (4-3-3): Jamie Bradley; Daniel Worthington, Billy Hodgkiss, Joe Cain, Jack McCallum (Conor Allen 46); Miles Lynch, Jack Dykes (Liam Moran 70), Corey Newman; Steven Dovey, Louis Saebe, Bradley Easey (Karolis Andriulionis 56).