Foster settled a tight and cagey third qualifying round tie at the Jakemans Community Stadium with a quality finish in the 52nd minute.
Following earlier victories over West Bridgford, Dunkirk and Mickleover Sports, United's win over the Spireites completed their journey to the competition proper.
Boston (3-4-2-1): Charlie Wilkinson; Bailey Dilley, Owen Sheriff, Ben Robson; Krisztian Gagyi (Charlie Earth 90), Mackenzie Burdass, Joe Melson, Zane Millar; Han Stevens (Logan Tate 84), Elliot Foster; Sam Harris. Subs (not used): Jake Henderson, Taylor Jaine, Ishaan Sumal, Finley Rodgers, Cameron Fox (gk).
Referee: Istvan Mod.
Attendance: 395.
PIC: Russell Dossett.