Nick Lovelace's side defended resolutely against their visitors from Northamptonshire, with goalkeeper Joe Douce performing well.
The result moved United on to four points from their opening three league fixtures.
Boston: Joe Douce, Alex Van-Tam, Jack Clayton, Charles Doble (Harry Gunthorpe 70), Reece Coy, Kirill Snikeris, Danny Walsh, Kye Rook, Matas Gecas, Cody Elgie, Kiaran Grove (Finley McDaid 60). Subs (not used): Leon Hagger, Jack Dixon, Tyler Griffin (gk).
Referee: Peter Brothwell.