The Pilgrims' youngsters were beaten at The Jakemans Stadium, despite a string of chances falling to Juris Kormis and Karolis Andriulionis.
United conceded once before half-time, with two further goals arriving after the break.
Boston (4-3-3): Sam Vince; Daniel Worthington, Miles Lynch, Todd Devlin, Jordan Sowerby; Aaron Eyett, James Reed, Lewis McKue; Leon Squire, Karolis Andriulionis (George Stainfield 64), Juris Kormis. Sub (not used): Charlie Melville.