Luke Horne and Taylor Jaine both scored twice, with Ezra Aaron and Will Langford on target too.
United led 3-1, 4-3 (at half-time) and 6-5 before AFC Fylde added their own sixth and seventh goals to seal an extraordinary victory.
Boston: Cameron Fox, Rueben Fogg, Josh Doran, Will Langford, Finley Ging, Taylor Jaine (Charlie Brooks 60), Joe Wilkinson (Nathan Bowen 55), Kris Zaluzinskis, Ezra Aaron, Lucas Turrell, Luke Horne.