York led 3-0 at the Jakemans Community Stadium – but United turned the tables to lead 4-3 through goals from Owen Sheriff (penalty), Krisztian Gagyi, Zane Millar and Elliot Foster.
City hit back with two late goals of their own to snatch a 5-4 win – with Bailey Dilley dismissed for the Pilgrims at the death.
Boston (3-4-2-1): Oliver Ford; Bailey Dilley, Owen Sheriff, Taylor Jaine; Krisztian Gagyi, Mackenzie Burdass, Joe Melson, Zane Millar; Han Stevens, Ben Johnson; Elliot Foster. Subs (used): Logan Tate, Sam Harris; (unused): Finlay Armond, Jake Henderson.
Referee: Alistair Wilson.