United trailed to Morgan Roberts’ 34th minute opener - but equalised in first half stoppage time through birthday boy Keaton Ward.
Jimmy Knowles ultimately won it for the Pilgrims - as United embraced jubilant scenes at the end in front of 900 travelling supporters.
The well-deserved win ensures United will be playing National League football in 2024-2025 - ending a 14-year wait for promotion from National League North.
United started well, with ex-Brackley man Martin Woods sailing an effort wide from 30 yards, but the Saints were soon on the front foot themselves, with Danny Newton's header brilliantly clawed aside by Cameron Gregory and Connor Hall seeing his rebound ruled out for offside.
Dylan Hill and Jordan Richards both sent glancing efforts off target before a Woods free-kick deflected off the wall and landed on the roof of the net.
Gregory made excellent saves to deny Roberts and then Tyler Lyttle - with the latter effort flying to safety off the post.
Brackley did edge ahead 11 minutes before the break when United failed to clear their lines and ROBERTS swooped to score from close-range.
The Pilgrims levelled in the third minute of added time when Brad Nicholson's long throw found its way to WARD inside the penalty area and he blasted through a crowd of bodies to restore parity.
United were the better side after the break and Danny Lewis had to make an early save to deny Knowles.
The game's defining moment arrived 13 minutes after the break when a marauding Jai Rowe was upended by a combination of Gareth Dean and Riccardo Calder and KNOWLES coolly sent Lewis the wrong way from the spot.
Late chances fell to substitute Michael Gyasi and then Knowles and while United had to withstand a Brackley onslaught, they did not give up a clear-cut chance and deservedly closed out promotion to the National League.
Brackley (3-4-1-2): Danny Lewis; Tyler Lyttle (Liam Cross 85), Gareth Dean, Zak Lilly; George Carline, Tommy O'Sullivan (Alfie Bates 71), Shepherd Murombedzi, Riccardo Calder; Morgan Roberts; Danny Newton, Connor Hall (James Armson 85). Subs (not used): Alex Gudger, Dan Turner.
Boston (3-4-1-2): Cameron Gregory; Zak Mills, Michael Bostwick, Brad Nicholson; Jai Rowe, Jordan Richards, Martin Woods (Michael Gyasi 84), Dylan Hill; Keaton Ward; Kelsey Mooney (Jacob Hazel 81), Jimmy Knowles (Deji Sotona 90). Subs (not used): Tom Leak, Sam Smart.
Attendance: 3,074 (900 visitors).
Referee: James Bancroft.