The Pilgrims took the lead three minutes before half-time through Jordan Tate and never looked back after the break.
Harry Vince and Connor Stocks were on target either side of a Peter Evison brace.
Boston (4-3-3): Harry Payne; James Gordon (Peter Evison 66), Callum Rodger, Bailey Forth, Jack Brown; Jordan Tate, Jack Withers, Harry Vince; Jenson Ball (Kofi Ross 49), George Smith (Connor Stocks 71), Ben Lawrence. Subs (not used): Oli Drummond, Elliot Andrew.
Referee: Trevor Basker.
Attendance: 131.