The Pilgrims led the National League U19 Alliance Academy Division North leaders 3-0 at half-time thanks to goals from Horne, Joe Wilkinson and Hugo Hunt.
Horne added two more goals after the break - the final effort from the penalty spot - to cap a memorable afternoon for the Pilgrims.
Boston: Cameron Fox, Oliver Fields, Josh Doran (Finley Ging 78), Will Langford, Ellis Perry-Burdett, Charlie Brooks, Joe Wilkinson (Jake Henderson 63), Kris Zaluzinskis, Lucas Turrell (Nathan Bowen 65), Hugo Hunt (JJ Ward 80), Luke Horne (Rueben Fogg 80).
Referee: Alistair Wilson.