The hosts were the first to threaten as winger Matt Lowe came close to notching an early opener.
He was teed up by Lee Ndlovu and advanced into the box at an alarming speed, but saw his shot blocked by a sliding Shane Killock.
Brackley’s Omari Sterling-James then embarked on a mazy run down the left before cutting in and drawing an impressive stop from Steven Drench with a curling effort.
Drench was called into action again when the resulting corner delivery landed at the feet of Oran Jackson, who stung the goalkeeper’s palms with a close-range strike.
The Saints were eventually rewarded for their pressure when veteran midfielder Carl Baker broke the deadlock. Brackley’s latest signing rifled into top corner from around 25-yards out, rendering a diving Drench helpless.
After taking the lead, Brackley continued to cause Bradford problems and Drench was forced to palm Lowe’s shot wide after the winger advanced unchallenged.
As the second-half entered its latter stages, Bradford sought to mount a comeback and demonstrated a quicker tempo in the final third. Oli Johnson lifted into the box from the left, but Jake Beesley failed to connect cleanly with the ball under pressure from Jackson and headed wide.
Gianluca Havern connected with Lewis Knight’s corner delivery with just a minute of the first-half remaining, but his powerful header found the wrong side of the post.
Saints skipper Gareth Dean then thwarted Beesley, making a last-ditch tackle that prevented Bradford’s marksman going one-on-one with Danny Lewis.
HALF-TIME: Brackley Town 1-0 Bradford (Park Avenue)
Lowe had proven to be a thorn in Bradford’s side throughout the first-half and his direct running created an opportunity within two minutes of the second-half beginning. He accelerated down the right flank before rolling the ball into the path of Baker, who saw his shot blocked by Havern.
James Armson then tried his luck from 20-yards but his tame effort was held comfortably by Drench.
Drench, however, was powerless to prevent Ndlovu’s header nestling in the back of the net after the forward met Shane Byrne’s cross.
Bradford embarked on a hunt for an opening as they attempted to claw their way back into the game, but both Jamie Spencer and Knight saw efforts blocked in the 18-yard box.
The hosts continued to pose an attacking threat despite their relatively comfortable lead and Lowe was denied by Drench after darting into the box from the right flank.
Brackley’s lead was eventually extended through Baker, who fired into the top corner from close-range after the ball was delivered to him on a plate by Lowe.
The visitors failed to produce a response in the final ten minutes as Brackley held strong and nullified the attacking threat in Bradford’s frontline.
FULL-TIME: Brackley Town 3-0 Bradford (Park Avenue)
Brackley Town: Lewis, Myles, G. Walker, Byrne, Jackson, Dean (c), Lowe, Armson (A. Walker 78’), Ndlovu (Nti 88’), Baker, Sterling-James (Fairlamb 68’).
Unused substitutes: Jeffers.
Bradford (Park Avenue): Drench, Ross, Lowe, Spencer, Killock (c) (Nowakowski 72’), Havern, Knight, Branson, Beesley, Johnson (Hurst 52’), Clee (East 78’).
Unused substitutes: Atkinson, Dawson.
Referee: Matt Russell