Trenerry’s long ball forward in the 11th minute was misjudged by his Curzon counterpart Chris Renshaw and ended up in the back of the net.
Luke Parkin also clipped the top of the crossbar for the visitors before skipper Dave Syers doubled the advantage just past the half-hour mark, heading in Lewis Turner’s cross to the far post.
The hosts’ 81st-minute consolation was scored by Tom Peers.
Despite that strike, Curzon were unable to push on, and failed to trouble the Farsley goal in the closing minutes. And it was Farsley who could have scored again. Substitutes Jacob Gratton and Harry Jessop linking up as the latter fired a strike inches over.
The victory means the Celts are now just one point behind second-bottom Guiseley, having played one game more.
The Lions were once again left to rue missed chances as they went down 1-0 at Leamington on Saturday.
Guiseley started brightly creating a number of chances. Dom Tear produced good skill and saw his shot well saved by Callum Hawkins.
George Cantrill then almost scored with a clearance that instead went just over the crossbar.
There was then a goalmouth scramble, but the Lions just could not get a crucial touch on the ball which would almost certainly have resulted in the opener.
The hosts meanwhile would put in a number of crosses that had to be dealt with but the scoreline remained goalless at the break.
As has been the case in some of the previous games, Guiseley were punished for not taking their chances when Devon Kelly-Evans gave the home side the lead with a powerful finish, after a long throw was not dealt with.
Guiseley tried to get back into the match and had a good opportunity when Josh Stones was fed through, but his effort went wide.
Stones would again go close late on, when on the angle he tried to find a team-mate but to no avail, in another frustrating moment during the game for the visitors.
The final actions of the game saw Leamington denied another goal, when Owen Mason did well to stop Kelly-Evans from doubling his tally for the day.
The result makes Tuesday night’s home game against fellow relegation-threatened AFC Telford United an absolutely vital match.
After the defeat, Lions’ joint-manager Marcus Bignot said: “It was a game of two halves, they survived the first and we just about didn’t in the second. It is important we show a reaction on Tuesday.”
Meanwhile, Bradford Park Avenue suffered a third straight league defeat – representing their worst losing streak of the season – after going down 2-1 at home to Gloucester.
Simon Richman raced on to a Lewis Knight through ball to cancel out Lucas Tomlinson’s opener for the visitors, only for Matt McClure to settle matters on 79 minutes.
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