Nick Lovelace's team were 2-1 victors at Rugby Borough – courtesy of first half goals from Stephen Pereira and Cody Elgie.
Rugby reduced the arrears on the hour mark – but United held on for a hard-fought away win.
Boston: Joe Douce, Harry Gunthorpe, Alex Van-Tam, Charles Doble (Jake Leggate 60), Dominic Chew (Lewis Horne 46), Reece Coy, Danny Walsh, Kye Rook, Stephen Pereira (Jaydon Sargent 65), Cody Elgie, Kiaran Grove. Subs (not used): Kirill Snikeris, Tyler Griffin (gk).
Referee: Carl Henry.