The Pilgrims trailed 2-0 at half-time in the encounter played on the new 3G surface at Skegness Sports Association.
Harrison Holland replied with eight minutes to play, but the Pilgrims were unable to find a leveller.
Boston (4-2-3-1): Oliver Swaby; Jamie Gaukroger (Harrison Holland 75), Taylor Gray, Callum Rodger, Jack Brown; Peter Evison, Jack Henton (Arkadiusz Michalczyk 50); Marshall Young, Jenson Bark, Ryan Pratt (Jenson Ball 30); Will Jackson.