A superb solo goal from Danny Greenfield put the Celts ahead a few minutes into the second half.
Danny Philliskirk scrambled the ball home from a corner to level matters on 78 minutes but resolute defence from Farsley ensured the point was secured, after a first draw this season.
The hosts generally looked the more dangerous in the first half and their first dangerous chance came on 23 minutes as Luke Burgess picked out Danny Lloyd but he shot straight at Darryl Ombang.
In the only other notable chance of a first half shy of goalscoring opportunities, Burgess gained possession but his curling effort was just wide of the far post.
The Celts came out firing after the interval and took the lead through a fantastic goal from Greenfield. The midfielder turned his man before producing a pin-point strike past Chris Renshaw to give Farsley the advantage on 48 minutes.
And it could have been 2-0 on 65 minutes had Isaac Assenso converted from a corner but he put the half-chance over the bar.
After Lloyd had seen his free-kick tipped over the bar by Ombang, the hosts drew level on 78 minutes from the resulting corner. After the ball had been swung in Philliskirk got his foot on the ball to poke it through a sea of players and past Ombang to make it 1-1.
Southport dominated the latter stages, particularly when Farsley were reduced to ten men after Ryan Watson limped off with an injury after all five substitutes had been used, but staunch defending saw the Celts ensure the point, under the guidance of Pav Singh for the first time.
The Celt Army are once again on their travels this Saturday, with a trip to Suffolk to face Vanarama National League new-boys Needham Market.
Farsley Celtic: Ombang, Turner (Hyde 45+1), Allan, Assenso, Sloane, Branson, B Atkinson, Watson, Greenfield (Fielding 87), Stephenson (Kiwomya 84), Campton-Sturridge (Youmbi 8 (Fox 64)).