Strikes from Zak Lilly and Morgan Roberts did the damage for the Saints early on - with Brad Nicholson reducing the deficit in first half stoppage time.
United dominated after the break, but were unable to turn their considerable territory and possession into gilt-edged chances.
The match had survived a 10.00am pitch inspection and the Saints were soon into their groove - taking an 11th minute lead when Tommy O'Sullivan's long throw found its way to LILLY who hooked home the opener.
Four minutes later, ROBERTS was threaded through and beat Cameron Gregory with a crisp, low drive.
Gregory subsequently denied Danny Newton and Alex Gudger within seconds of each other as Brackley threatened to cut loose. He then tipped a deflected Riccardo Calder cross wide for a corner.
United reduced the arrears two minutes into first half stoppage time when NICHOLSON stabbed the ball home from close-range after Jordan Richards had crossed from the right.
Sam Smart was introduced on the hour mark and he was soon into the thick of the action, with Brackley keeper Danny Lewis keeping out Deji Sotona's swerving drive.
The Pilgrims enjoyed plentiful possession in the second half - but Lewis only really had one further save to make from Keaton Ward.
Brackley (3-5-2): Danny Lewis; Zak Lilly, Gareth Dean, Alex Gudger; Cosmas Matwasa (Tyler Lyttle 70), Tommy O’Sullivan, Shepherd Murombedzi, Dominic McHale (James Armson 73), Riccardo Calder; Danny Newton, Morgan Roberts (George Carline 90). Subs (not used): Dan Turner, Layton Love.
Boston (4-4-2): Cameron Gregory; Zak Mills (Sam Smart 60), Michael Bostwick, Tom Leak, Brad Nicholson; Deji Sotona, Dylan Hill, Jordan Richards, Keaton Ward; Jimmy Knowles, Jacob Hazel. Subs (not used): Ethan Sephton, Keziah Martin, Sam Essien, Jake Lovelace (gk).
Referee: David Jones.
Attendance: 641.
PIC: Chris Bray.