First half goals from Owen Sheriff and Krisztian Gagyi sealed the deal for Ray Power's side in the northeast.
Gagyi finished the match between the posts after goalkeeper Jake Lovelace was substituted through injury on the hour mark.
Boston (3-4-2-1): Jake Lovelace (Jake Higginbottom 60); Taylor Redman, Owen Sheriff, Taylor Jaine; JJ Ward (Joel Smith 75), Han Stevens, Jake Henderson, Josh Doran; Krisztian Gagyi, Lucas Turrell (Dominic Chew 85); Flynn Slater.