The sides fought out their second goalless first half of the week – but Johnson’s long-range strike soon handed United the lead after the break.
Chester struck back with two goals to clinch all three points.
Boston (3-4-2-1): Oliver Ford; Bailey Dilley, Owen Sheriff, Ben Robson; Krisztian Gagyi, Mackenzie Burdass, Finlay Armond, Zane Millar; Han Stevens, Ben Johnson; Elliot Foster. Subs (used): Sam Harris, Logan Tate, Jack Waddington; (unused): Joe Melson.
Referee: Michael Brader.