The Pilgrims held a 2-0 lead against Mansfield Town Brooksby before being pegged back to 2-2 — only to roar back and claim a 4-2 win at Freiston FC.
Elliott Ramsden and Mido Turki were the Pilgrims' other goalscorers.
Boston (4-3-3): Seth Greeves; Jamie Gaukroger, Lewis Bontoft, Harry Cranfield, Nathan Stevens; Marc Tucker (Brendan Oldham 65), Marshall Young, Mido Turki; Jenson Bark, Harrison Holland, Elliott Ramsden. Sub (not used): Xander Crashley.