Despite a handful of early Farsley chances, the visitors took a 26th minute lead through Zac McEachran.
Phil Croker doubled their lead straight after the break although Farsley pulled one back almost immediately after a phenomenal long-distance strike from Joao Silva.
However Josh Ashby’s 72nd minute strike guaranteed the win for Oxford which in turned ensured their status at step 2 for next season.
Farsley controlled proceedings for the first 20 minutes of the game and fired an early warning sign as Cole Hyde saw his effort from a narrow angle kept out by Laurie Walker on the 4th minute.
Walker then had to scramble low to his right to deny Manny Mampala’s low curling free kick on 14 minutes before Justin Iwobi blazed over on the edge of the box from Dylan Youmbi’s lay-off a minute later.
But Oxford punished those missed chances when, just seconds after a goalmouth scramble following a corner which saw them almost force the ball over the line, the ball was laid off to McEachran who picked his spot in the corner of the goal with a crisp finish.
Joao Silva produced a sensational strike from a tight angle a couple of minutes before the break but it was ruled out by the assistant referee’s offside flag.
The Oxfordshire side landed a hammer blow two minutes after the interval as Croker was left unmarked and nodded home their second from a corner.
The two goal advantage didn’t last long though as soon after the restart, the ball was played to Silva and he unleashed a thunderbolt strike from well over 25 yards which flew into the top corner to bring Farsley back within a goal, in emphatic fashion.
City were still looking the more likely to score next though, especially with lively left winger Lewis Coyle causing plenty of issues. He first fed Josh Parker but the midfielder was denied by a good save from Brook before another incisive ball needed an intervention from Cole Hyde – the left back’s touch thankfully taking the ball just to the outside of the post.
Then on the hour, Coyle’s low shot curled wide of the post before a quick free-kick routine from the visitors saw McEachran get a sight of goal but his effort was cleared off the line by a Farsley defender.
But their pressure paid off as a third goal arrived on 72 minutes when Jayden Carbon pulled the ball across from the bi-line and Ashby converted with a powerful finish from close range.
David Stockdale’s Farsley continued to battle inside the final 15 minutes of the game but to no avail, meaning they ended the evening 17 points away from safety, with only 15 now left to play for, signaling the Celts’ first relegation in 17 years, when they fell out of the Conference back in April 2008.
There are still five games left to play though, with Saturday’s trip to Darlington next on the agenda for the young Farsley side.
Farsley Celtic: Brook, Abankwah (Ameho 85), Janneh, Polwarth, Bumhira, Hyde, Youmbi, Mampala, Kondolo, Iwobi (Monteiro 80), Silva.
Sub not used: Pristley-Standing.