After a goalless first half, George Glendon gave the visitors a 63rd minute lead in Buxton.
Justin Iwobi’s fantastic finish drew Farsley level inside the final ten minutes and it looked as though the Celts would claim their first point in almost three months, but Scott Duxbury’s 91st minute header cruelly snatched that point away.
Joao Silva’s early free kick tested Radcliffe goalkeeper Matheusz Hewelt in the opening couple of minutes before Farsley’s shot stopper Will Brook was called into action to deny Anthony Dudley with a fine save on 21 minutes.
Radcliffe came close again a few minutes later as Matt Carson’s free kick brushed the side netting before Dylan Youmbi went just as close for the Celts, with a tepid first half drawing to a close goalless.
Corbett and Tom Walker both went close to ending the stalemate in the opening encounters of the second half and they did snatch the opener shortly after the hour mark, in somewhat fortuitous circumstances.
An initial shot was blocked but the ball dropped right to the feet of Glendon who, from 12 yards out, made no mistake in slotting past Brook.
Glendon almost added a second to his and Radcliffe’s tally on 68 minutes as his cross-come-shot clipped the outside of the post before being scrambled away from danger.
Farsley remained determined and struck a deserved equaliser when Iwobi pulled off a fantastic finish to bury the ball into the bottom corner to draw the Celts level.
Stout defending from Farsley followed, with Brook pulling off an excellent save to flick substitute Jordan Hulme’s effort over the bar before Isaac Abankwah bravely put his body on the line to block Matt Sargeant’s powerful effort on the goal-line from point-blank range.
However in a cruel for a determined Celts side, Duxbury was allowed a free header and picked out the corner of the goal to nod Radcliffe a late winner, also securing their survival in the National League North for next season.
Farsley Celtic: Brook, Abankwah (Bumhira 88), Janneh, Polwarth, Monteiro (Ameho 90+3), Hyde, Youmbi, Mampala, Kondolo (Priestley-Standing 90+3), Iwobi, Silva.
