Iffy Allen and Seth Chambers had given the visitors a 2-0 advantage although Robbie Fox pulled a goal back for the Celts before the break.
However further second half goals from Allen and Chambers, coupled with efforts from Reggie Lambe and Liam Cross saw the Suffolk side to a comfortable victory.
Farsley, who were today managed by Izzy Roads and Phil Lake in the absence of Neil Redfearn and Pav Singh, were behind after 10 minutes after Allen got on the end of Jacob Lay’s pass to net his first goal for Needham Market.
Their lead was doubled 10 minutes later as Allen fed Chambers who flew in down the right wing and found the goal, despite the best efforts of Cole Hyde.
Farsley’s brightest moment of the game came on 41 minutes as Fox drove into space before smashing home into the top corner to reduce the deficit.
But the visitors notched again eight minutes after the break as Allen added his second with a finish into the top left corner.
Allen was causing all sorts of problems and he provided an excellent cross into Lambe who added a fourth on 59 minutes, rubber-stamping the win for The Marketmen.
A fifth was added three minutes later when captain Kieran Morphew played the ball in to Chambers who secured his brace with a smart finish.
The rout was completed on 77 minutes as Tevan Allen’s cross was headed in at close range by Cross, which compounded out an all-round difficult afternoon for the Celt Army.