Top goalscorer Luke Horne, rested on the bench after his exertions for Grantham Town the previous night, emerged as a second half substitute to grab the only goal of the game in the 73rd minute.
The result rounded off a perfect month for Ray Power's Pilgrims, following earlier wins over York City, Chester FC and Altrincham.
Boston: Cameron Fox, Ellis Perry-Burdett, Josh Doran, Will Langford, Finley Ging, Taylor Jaine, Rueben Fogg (Charlie Brooks 83), Kris Zaluzinskis, Jake Henderson, Nathan Bowen (Luke Horne 56), Joe Wilkinson (Oliver Fields 69).