Luke Jackson had handed Stockport a first half lead at Stockport Sports Village.
An Elliot Foster double and a Ben Johnson strike sealed a richly-deserved win for Mark Thompson's side.
Boston (3-4-2-1): Oliver Ford; Bailey Dilley, Owen Sheriff, Ben Robson; Logan Tate, Han Stevens, Mackenzie Burdass, Zane Millar; Finlay Armond, Ben Johnson; Elliot Foster. Subs (used): Krisztian Gagyi, Sam Harris, Taylor Jaine, Jack Waddington.
Referee: Roger Andrew.