Miller and defender Scott Garner were the most senior players in a United team which finished the match with 10 teenagers on the pitch.
Jamie McGhee handed the Gingerbreads a 17th minute lead from distance and despite Miller's 55th minute leveller, Grantham secured the win when Karl Demidh struck 13 minutes from time.
Boston (4-4-2): Sam Vince; Niall Delahoy (Louis Saebe 75), Scott Garmer (Ollie Price 64), Elliott Green (Aaron Eyett 57), Grant Butler; Jordan Nuttell, Indy Aujla (Jacob Pease 82), Kieron Elliott, Billy Bennett (Leon Squire 82); Charley Sanders, Ricky Miller (Ngoni Dongo 66). Sub (not used): Andy Hewitt (gk).
Referee: Josh Smith