The Pilgrims found themselves 3-0 down at half-time in the National League U19 Alliance Academy Division North encounter - and conceded once more after the break.
United are back in action on Friday against Notts County.
Boston (3-4-2-1): Jake Lovelace; Taylor Jaine, Owen Sheriff, Lucas Stubbs (Taylor Redman 46); JJ Ward (Jack Waddington 60), Will Langford (Lucas Turrell 46), Jake Henderson, Josh Doran; Krisztian Gagyi (Jake Higginbottom 70), Han Stevens; Flynn Slater. Sub (not used): Cameron Fox (gk).
Referee: Istvan Mod.