The Pilgrims, having already lost 5-1 to opponents Kidderminster Harriers in the League Cup earlier in the season, were beaten 4-1 in the Academy Cup first round tie.
Finlay Armond scored United's second half consolation effort.
Boston (4-2-3-1): Jake Frestle; James Mallender (Ben Johnson 80), Harry Cranfield, Daniel Fisher, Joe Hardstaff; Brogan Horniman, Finlay Armond; Jamie Gaukroger, Ashton Taylor, Xander Crashley; Will Jackson. Sub (not used): Craig Forbes.
Referee: Ian Ruddock.