The Pilgrims prevailed 10-0 at Freiston FC with Adams leading the way with a quintet of strikes, including one penalty.
George Hobbins also scored a penalty on his way to a hat-trick, with Ben Lawrence and Harry Vince on target too.
Boston (4-3-3): Harry Payne; James Gordon (Connor Stocks 46), Jack Withers, Bailey Forth, Callum Rodger; Peter Evison (George Hobbins 46), Harry Vince, Jack Brown; Ben Lawrence (Jenson Ball 46), Liam Adams, Haydn Havard (Oli Drummond 46).