The Pilgrims extended their unbeaten start to the National League U19 Alliance Academy Division North campaign courtesy of Horne's brace on 39 and 47 minutes.
Fylde were handed a lifeline in the 82nd minute when Taylor Jaine headed into his own net - but United held on.
Boston: Cameron Fox, Ellis Perry-Burdett, Josh Doran, Will Langford, Finley Ging, Taylor Jaine, Rueben Fogg (Hugo Hunt 74), Kris Zaluzinskis (Rhys Smaller 88), JJ Ward, Joe Wilkinson (Jake Henderson 63), Luke Horne (Charlie Brooks 89).
Referee: Ian Ruddock.