Robbie Fox had got the Celts off to an excellent start with his header on 16 minutes giving Pav Singh’s side the advantage.
With a barrage of attacks in the second half, Farsley defended stoutly but substitute Jez Abbey found a late equaliser as the game headed into stoppage time.
Farsley were dealt an early setback in the tie with captain Conor Branson forced off inside the first ten minutes, with the skipper set to be added to the club’s lengthening injury list with a suspected rib injury.
But the Celt Army responded in style when they netted the game’s opening goal as towering forward Fox used his height to his advantage by heading in the opening goal.
There was little by way of goal action for much of the first half though Celtic had a half-chance to extend their lead on 33 minutes when Sam Fielding sent in an incisive cross-field ball into the Brackley box but Bailey Sloane couldn’t direct a tricky dropping ball goalwards with his first-time effort.
Farsley’s on loan goalkeeper Kieran Flavell pulled off two excellent saves before the break, firstly denying Matt Lowe and then a few minutes later Gaz Dean, with Connor Hall putting his shot wide of the target from the following corner.
Brackley made a quick start to the second half and only a goal-line header from Sloane prevented them from levelling as he headed a wind-assisted cross off the goal line.
Flavell continued to earn his corn in the Farsley goal, firstly denying Lowe for a second time before he then kept out Shane Byrne’s long-distance free kick.
The shot-stopper showed more great reflexes to react quickly to block the ball as it flew through a sea of players, before Dean saw his follow-up shot blocked by a Farsley defender.
The Celt Army could then have sealed victory as the game ticked into stoppage time as on-loan Wigan Athletic midfielder Finn O’Boyle showed great skill to round a defender and then the goalkeeper but Morgan Roberts crucially made a vital goal line block to keep Brackley in the fight.
And the Northamptonshire side dealt Farsley a cruel blow three minutes into stoppage time as Abbey’s shot bounced in off the crossbar to give The Saints a point, which on the balance of play, they probably deserved.
Farsley Celtic: Flavell, Hyde, Walker, Misambo, Abankwah, Sloane (Ferguson 90), Branson (Kondolo 9 (Silva 60)), Fielding, O’Boyoe, Atkinson, Fox.
Subs not used: Campton-Sturridge, Pickard.