Doubles from Jordan Tate, Harry Vince and Jenson Ball, plus single strikes from Bailey Forth, George Hobbins and Callum Rodger sealed United's emphatic victory.
The Pilgrims' fourth qualifying victory secured in place in Friday's first round draw.
Boston (4-3-3): Harry Payne; James Gordon, Jack Withers, Bailey Forth, Callum Rodger; Peter Evison, Harry Vince, Jordan Tate (Brian Tumfour 79); Ben Lawrence (Jenson Ball 70), George Smith (George Hobbins 50), Jack Brown. Sub (not used): Arkadiusz Michalczyk.