A low-key affair saw the real chances arrive in the closing stages, with Lee Ndlovu and David Pitt firing off target for the Saints and United's Jay Rollins and Mani Dieseruvwe being denied in spectacular fashion by home keeper Laurie Walker.
The result moved the Pilgrims to within touching distance of mathematical safety with five games to play.
Adam Murray had made an enforced change ahead of kick-off, with Shane Clarke replacing the unavailable Adam Chapman.
Brackley enjoyed the early territorial advantage and Shane Byrne lifted a fourth minute drive marginally too high from distance.
Jack Broadhead's header was blocked on the line at the other end by Matthew Barnes-Homer before Ross Durrant produced fine saves to keep out a potential Nat Brown own goal and Byrne's goalbound free-kick.
Jan Yeomans succumbed to a head injury at half-time and was duly replaced by fit-again Josh Robinson.
Broadhead blasted wide from distance at the beginning of the second half, while Brown's header dropped wide following substitute Alex Simmons' free-kick delivery.
Laurie Walker excelled to deny sub Lewis Hilliard from close-range following Rollins' cutback but the hosts subsequently wasted two glorious chances with Ndlovu clearing the crossbar and Pitt dragging an effort across goal and wide.
It was left to the home custodian to deny United all three points with Rollins' long-ranger tipped wide and then Dieseruvwe's header being palmed over as Brackley held on for a share of the spoils.
Brackley (3-4-3): Laurie Walker; Gareth Dean, Jordan Gough (David Pitt 73), Alex Gudger; Ellis Myles (James Clifton 74), Adam Walker, Shane Byrne, Glenn Walker; Lee Ndlovu, David Moyo, Matthew Barnes-Homer (James Armson 50). Subs (not used): Matt Lowe, Steve Diggin.
Boston (4-2-3-1): Ross Durrant; Kalern Thomas, Tom Batchelor, Nat Brown, Jan Yeomans (Josh Robinson 46); Shane Clarke, Jack Broadhead; Jay Rollins, Harry Vince (Lewis Hilliard 62), Louis Briscoe (Alex Simmons 50); Mani Dieseruvwe. Subs (not used): Colby Bishop, Charlie Gatter.
Referee: Chris Pollard.
Attendance: 333.