Fylde raced into an early three-goal lead on the Jakemans Community Stadium 3G - with JJ Ward cutting the deficit before half-time.
The Coasters added a further goal before the break - and two more in the second half.
Boston (4-3-3): Jake Lovelace; Taylor Redman, Oskar Rajski, Taylor Jaine, Lucas Stubbs (Josh Doran 46); Rueben Fogg (Jack Waddington 46), Han Stevens, Jake Henderson (Mark Williams 67); JJ Ward, FLynn Slater, Patrik Bad (Krisztian Gagyi 46). Sub (not used): Kelton Robinson.
Referee: Ian Ruddock.