The Pilgrims led at half-time courtesy of Tom Wilkinson's 42nd minute strike but Wilkinson was denied from the penalty spot by Fylde keeper Ben Wilcock, while United's Jake Frestle similarly kept out the Coasters' Sheldon Green from the spot.
Harry Brown equalised with 13 minutes to play, Robbie Parker struck a minute later and Green capped a man-of-the-match performance with Fylde's third five minutes from time.
Boston (4-3-3): Jake Frestle; Nathan Stevens, Harry Cranfield, Daniel Fisher (Joe Hardstaff 83), Jordan Elston; Finlay Armond (Dan Richards 66), Brogan Horniman, Will Jackson; Jamie Gaukroger, Tom Wilkinson, Xander Crashley (Henry Beedham 83). Subs (not used): Ben Johnson, Arron Bailey.
Referee: Alistair Wilson.