The Pilgrims' consolation goal came from half-time substitute Krisztian Gagyi.
United's away day woes were compounded by Taylor Jaine's dismissal for a second yellow card.
Boston (3-4-2-1): Jake Lovelace; Oskar Rajski (Lucas Stubbs 70), Owen Sheriff, Taylor Jaine; JJ Ward (Kyle Featherstone 73), Jake Henderson (Taylor Redman 60), Rueben Fogg, Josh Doran (Krisztian Gagyi 46); Han Stevens, Jack Waddington (Rohann Boughey 75); Flynn Slater.