Luke Horne gave the Pilgrims a second half lead – but they conceded three times before the final whistle to lose to the northeast side.
It was Blyth's second win at the Jakemans Community Stadium inside three weeks, following a 5-2 success in the Academy Cup at the end of February.
Boston: Daniel Martin, Ellis Perry-Burdett, Josh Doran, Will Langford, Finley Ging, Charlie Brooks, Nathan Bowen (Dexter Tomlinson 80), Kris Zaluzinskis, Joe Wilkinson (Rueben Fogg 55), Lucas Turrell (Hugo Hunt 60), Luke Horne.
Referee: Peter Brothwell.