Leading 2-0 early on courtesy of an Aaron Eyett strike and an own goal, United were pegged back by Adam Webb in the 32nd minute but added their third goal on the stroke of full-time through substitute Juris Kormis.

The Pilgrims will now meet Luton Town (at home) in the first round, with a possible trip to Tranmere Rovers awaiting the winners in round two.

Boston (4-3-3): Sam Vince; Daniel Worthington (Joe Searson 46), Josh Spencer, Ollie Price, Jordan Sowerby; Miles Lynch, Jacob Pease, Aaron Eyett; Leon Squire (Juris Kormis 81), Louis Saebe (Steven Dovey 80), Bradley Easey. Subs (not used): Charlie Melville, Billy Hodgkiss.

Referee: Jack Forder

Attendance: 176