The Pilgrims put up a solid showing against higher ranking opposition but were eventually undone by Solomon Miles' 75th minute strike.
United's woes were compounded by a serious knee injury sustained by full-back Joe Hardstaff in the closing stages.
Boston (4-3-3): Jake Frestle; Joe Hardstaff (Jake Henderson 90), Bailey Dilley, Brogan Horniman (Taylor Jaine 53), Ben Robson; Lewis Allen (Jack Bastos 74), Finlay Armond, Jack Waddington; Ashton Taylor, Tom Wilkinson, Ben Johnson. Sub (not used): Tom Ridley.
Referee: Istvan Mod.
Attendance: 125.