George Hobbins handed the Pilgrims a first half lead at Tattershall Road and Liam Adams struck again before the break to put Boston firmly in control.
The Pilgrims had to withstand some sustained Basford pressure after the interval but Adams’ 82nd minute free-kick wrapped up the points.
Boston (4-3-3): Harry Payne; Jack Brown (Jenson Ball 84), James Gordon, Jack Withers, Callum Rodger; Jack Dykes (Maison North 73), Jordan Tate, Peter Evison; Liam Adams, George Hobbins (Jack Henton 87), Haydn Havard (Arkadiusz Michalczyk 87).