Droylsden claimed their first away win of the year but barring a miracle they will still be relegated from the Blue Square Premier.
With five games left to play they trail 20th-placed Weymouth by 15 points and have a vastly worse goal difference.
They went in front when Kevin Lynch headed home a 12th-minute corner.
Damien Reeves levelled the scores four minutes later with a smart finish into the bottom corner, but Terry Fearns headed a second-half winner.
Farsley Celtic: Aspden, Downes, Jackson (Ryan Serrant 41), Santos, Scott McNiven, Stamer (Tuck 66), Knowles, Bambrook, Prendergast, Reeves, David McNiven, Ryan Serrant (Heath 88). Subs Not Used: Watson, Torpey.
Goals: Reeves 16.
Droylsden: Phillips, Roche, Munroe, Halford, Newton, Lynch (Murphy 77), Mackin, Burberry, McGuire (Talbot 69), Fearns (Strong 90), Denham. Subs Not Used: Dugdale, Ellis.
Booked: Lynch.
Goals: Lynch 12, Fearns 86.
Att: 480
Ref: RJ West (Hull).
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