The Pilgrims had previously lost all four FA Youth Cup encounters on spot-kicks - but bucked the trend courtesy of two excellent Lovelace saves against Grantham Town, allied to successful penalties from Han Stevens, Rueben Fogg, Liam Sutton and JJ Ward.
Krisztian Gagyi handed United an early lead but they needed a deflected Mark Garner leveller seven minutes from time to force penalties after visiting replies from Brook Isherwood and Freddie McGrady.
Boston (4-3-3): Jake Lovelace; Finley Rodgers (Liam Sutton 82), Taylor Jaine, Taylor Redman, Josh Doran; Jake Henderson (Mark Garner 72), Han Stevens, Rueben Fogg; Patrik Bad (Flynn Slater 61), Krisztian Gagyi, JJ Ward. Subs (not used): Lucas Stubbs, Kelton Robinson, Cameron Smith, Cameron Fox (gk).
Referee: Ellis Mills.
Attendance: 285.