The Pilgrims were already on top by the time the hosts were reduced to 10 men a minute before half-time following a professional foul on striker Tom Wilkinson.
Midfielder Jack Waddington scored United's first two goals in the 51st and 66th minutes before Ben Johnson's 77th minute clincher. Josh Shaw reduced the arrears for the hosts two minutes from time after defender Brogan Horniman had been forced off with a shoulder injury to ensure the match finished 10-a-side.
Boston (4-1-4-1): Jake Frestle; Joe Hardstaff, Owen Sheriff, Brogan Horniman, Ben Robson; Joe Melson; Ashton Taylor (Zane Millar 68), Finlay Armond, Jack Waddington (Mackenzie Burdass 74), Ben Johnson; Tom Wilkinson (Charlie Earth 84). Subs (not used): Elliot Foster, Peter Wynn-Jones, Bailey Dilley, Charlie Wilkinson (gk).
Referee: Daniel Ghent.