In an afternoon of ups and downs the Pilgrims leapfrogged Kettering Town to claim seventh.
Jake Wright jnr and Danny Elliott netted the vital goals for the Pilgrims, who moved up following Kettering Town's 1-1 at Curzon Ashton
But after a nervy wait for the Poppies' result to filter though, the celebrations began for the away side.
The hosts - who looked relegated with minutes to go - were already having their fun after Alfreton's late goals sunk Guiseley.
The strikers get the accolades, the Pilgrims' side all played their part in a resolute defensive display as the last three games' habit of letting a lead slip were lost.
The Pilgrims began with purpose, knowing that if Kettering were to win they'd have to better the Poppies' score by two goals.
Scott Garner flashed a second-minute header wide and Elliott flashed Wright jnr's cutback over.
But the hosts - fighting for survival - carved out opportunities of their own.
Ex-Pilgrims Frank Mulhern saw a 20-yard effort collected by Marcus Dewhurst before his dipping volley landed on the roof of the net.
Femi Seriki did enough to put Parkin off as he looked set to head Farsley ahead - before it was advantage Boston.
Seriki's long throw was flicked on by Luke Shiels, Wright collecting and volleying home on the turn to hand the visitors as 37th-minute lead.
Paul Green couldn't find the necessary connection as two golden opportunities to add to the lead went begging.
Farsley came out swinging after the interval, Dewhurst collecting Mulhern's effort on the line and forced to divert Luke Parkin's long ranger.
As news of Curzon taking the lead against Kettering filtered through, the Pilgrims attempted to stifle the game - the sensible thing to do but not good for the nerves as Frank Mulhern rattled a free kick inches wide.
Celtic now had to go for it as Guiseley led at Alfreton and Farsley dropped into the relegation zone.
And go for it they did as Jerome Greaves' header landed inches over the Boston bar and Kennedy Digie volleyed over from six yards out.
But it was Boston who netted number two of the afternoon, Elliott getting a toe on the ball to divert Scott Duxbury's low cross into the roof of the net with seven minutes to play.
FARSLEY: Robson, Digie, Atkinson, Clayton, Syers (Greaves 32), Gratton, Turner, Spoencer, Hayhurst, Mulhern, Parkin; Subs (not used): Trenerry, Drake, Ingham, Malumo.
PILGRIMS: Dewhurst, Duxbury, Garner, Shiels, Green, Wright jnr (Massanka 30), Elliott, Wright snr, Abbott, Byrnbe, Seriki; Subs (not usded): Thanoj, Ferguson, Preston, Sault.
REF: David McNamara.