The Pilgrims trailed 1-0 at half-time, with Horne levelling five minutes after the break.
Gateshead re-asserted their lead midway through the second half but Horne had the final say from 12 yards.
Boston: Daniel Martin, Rueben Fogg (Jake Henderson 85), Josh Doran, Will Langford, Ellis Perry-Burdett, Charlie Brooks, Ezra Aaron, Kris Zaluzinskis, Luke Horne, Lucas Turrell, JJ Ward (Hugo Hunt 70). Subs (not used): Dexter Tomlinson, Reece Coy, Flynn Slater.
Referee: Peter Brothwell.