The Pilgrims trailed 1-0 at half-time but conceded twice straight after the break to present themselves with a mountain to climb.
Although captain Daniel Worthington netted for the Pilgrims, Town added two late goals to secure a comfortable victory at RFA College Cranwell.
Boston (3-5-2): Jamie Bradley; Billy Hodgkiss, Ollie Price, Joe Cain; Daniel Worthington, Miles Lynch (Jack Dykes 50), Liam Moran, Corey Newman, Bradley Easey (Scott Floyd 66); Louis Saebe, Steven Dovey (Jack Foyster 66). Subs (not used): Daniel Moulds, Conor Allen.