Goals from Martyn Woolford and substitute Craig Farrell were enough to secure York City passage through to the quarter-finals of the FA Trophy.
* Click here for enjoy a picture slideshow of match action from Farsley Celtic v York City. Strong winds and a tentative approach from both sides made the opening exchanges a dour affair.
* Injury is a real pain for Farsley Celtic skipper Ryan Crossley: Click here for full interview.The home side's first effort came in the 13th minute when Damian Reeves raced onto Simeon Bambrook's lofted through ball.
But the striker sliced his attempted lob over the onrushing Tom Evans into the stands.
York soon responded however with a fine solo run from striker Richard Brodie down the right flank who delayed his cross far too long allowing goalkeeper Curtis Aspden to smother the ball.
The Celts nearly made them pay for it when Evans dropped a catch from Bambrook's free-kick and left James Knowles with an open goal.
However the referee blew his whistle for a foul to save the keeper's blushes.
Farsley then had a solid penalty appeal turned down for handball and as the hosts continued to press, Daniel Parslow's last ditch challenge prevented Bambrook a clear run-in on goal before Woolford squandered a great chance from 10 yards.
Woolford made amends quickly after the break scoring with an exceptional free kick in the 50th minute after being brought down by Knowles.
The former Frickley man dispatched a left-footed free-kick round the Farsley wall into the bottom hand corner of the net to register his fourth goal in four games.
The home side responded positively however and had two efforts cleared off the line by their former player Anthony Lloyd, the first from substitute Tristam Whitman's shot and the second from Amjad Iqbal's downward header.
York City manager Colin Walker then brought on Onome Sodje and he forced two saves from Aspden in the last 15 minutes, the first after he charged down the keeper's clearance and the second following Iqbal's wayward back-pass.
With Sodje running the Celts ragged, the home-side were unable to get anywhere near the Minstermen's goal and any hopes of a replay for them were dashed in the 89th minute.
A mix-up in defence between Craig Bentham and Mark Jackson meant that a blocked clearance fell kindly to Farrell who smashed home from 6 yards past the helpless Aspden to secure a deserved victory.
Walker said after the game: "It was a very scrappy game but because it's a cup game you've just got to get the victory and get into the next round and we're happy to do that."
Farsley's number two Neil Parsley said: "It was a really tight game with few chances for either side. There was nothing in it and the second goal was a sickener really in terms of the score-line."
Farsley Celtic: Aspden, Jackson, Iqbal, Knowles, Bambrook, Reeves, Watson, McNiven, Downes, Bentham, Gardner. Subs Not Used: Grant, Stamer, Whitman, Torpey, Heath.
York: Evans, Elliott, McGurk, Parslow, Panther, Woolford, Brodie, Wroe, Purkiss, Lloyd, Fry. Subs Not Used: Sodje, Farrell, Mimms, Turnbull, Beadle.
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