Reiss Harrison opened the scoring the Minstermen in the seventh minute and Kai Ventura added a second after 59 minutes.
United handed a debut to under-16s player Bailey Dilley during the second half.
Boston (3-5-2): Jake Frestle; Brogan Horniman, Daniel Fisher, Nathan Stevens (Bailey Dilley 80); James Mallender, Finlay Armond, Jamie Gaukroger, Ashton Taylor (Josh Burkitt 70), Joe Hardstaff (Tom Wilkinson 57); Will Jackson (Ben Johnson 88), Xander Crashley. Sub (not used): Craig Forbes.