Despite Dave Syers’ header levelling matters after Josh Hancock’s opener from the spot, things started to go south for the Celts with Craig Mahon and Hancock netting his second before the break.
A second half double from Tom Peers put The Nash out of sight, before Frank Mulhern added a late consolation penalty as Farsley returned to Yorkshire empty handed.
After Max Dearnley had to make a strong double-save inside the opening minute, Curzon were given another early opportunity to open the scoring as they were awarded an 11th-minute penalty.
Tom Allan fouled an attacker on the edge of the box, and the referee pointed to the spot, after initially signalling for a free-kick. Hancock coolly slotted down the right for 1-0.
Farsley were quick to respond as Syers met Kian Scales’ cross with an excellent header to put the ball past Chris Renshaw to level matters.
But the hosts bagged again just after the half-hour mark, as Mahon fired home after a goal mouth scramble couldn’t be cleared by the Farsley defence.
And two became three on 42 minutes as Curzon went into the break with a commanding lead. A slip from Adam Clayton put Hancock in down the left and he fired past Dearnley.
The Tameside outfit netted again six minutes after the break as Peers netted his first of the second half after an error from Dearnley saw him spill the ball into his own goal.
The gap was then extended to four on 65 minutes with Peers bagging his second by firing into the bottom corner.
The Celts were handed a 75th minute penalty after Tom Allan was felled in the box, and Mulhern converted down the left to pull one back for Russ Wilcox’s side.
Farsley had a few late chances to close the gap even further, firstly sub Carlton Ubaezuonu couldn’t quite get enough on the ball to poke it past Renshaw before Luke Parkin fed in Bobby Johnson just inside the box, but the midfielder fired over.
Curzon Ashton: Renshaw, Poscha, Matthews, Walker (Richards 90+1), Peers, Hancock (Jessop 76), Hayhurst, Waring, Mahon, Barton, Campbell.
Subs not used: Hall, Braithwaite, Armstrong.
Farsley Celtic: Dearnley, Turner (Atkinson HT), Butler, Clayton, Allan, Butroid (Parkin 64), Scales, Johnson, Syers (Ubaezuonu HT), Spencer, Mulhern.
Subs not used: Teale, Assenso
Referee: David McNamara