A resilient Salisbury launched a classic second-half comeback through Josh Hedges and Nathan Odokonyero after conceding to Farnham's first chance of the game.
Farnham Town opened the scoring in the 8th minute with a familiar face to travelling Salisbury fans, Rakish Bingham, who scored his winner away for Farnborough last season.
The hosts launched a counter-attack down the right-hand side through Conrad Hunt, who put a powerful ball low across the box for Bingham to slot into the bottom-left corner, out of reach of Will Henry.
Salisbury refused to bury their head in the sand, however, as Robbie Gallagher quickly won a free-kick, which became a running theme.
Josh Hedges grabbed the opportunity to shoot from the tight angle and catch the keeper off-guard, but Michael Eacott managed to claw the attempt out before it hit the roof of the net.
After the interval, Farnham had a brilliant opportunity to double their advantage after an interception in the middle of the park allowed Billy Clifford to release new signing George Alexander, who tried to round Will Henry, but the Whites number one snatched it from his touch to keep the score at 1-0.
Just a minute later, Robbie Gallagher worked hard down the left flank and released a pass to Josh Hedges, who avoided a sliding challenge at the top of the box and bent an effort into the bottom-right corner for Salisbury's equaliser.
Ten minutes on, Hedges became the talismanic figure once again, picking up the ball and weaving inside before unleashing Odokonyero to his right, who nutmegged the keeper to give Brian Dutton's side the lead.
There was almost last-minute carnage as one Farnham attacker managed to round Will Henry as the ball bobbled in the box, but a shot was unable to be put away and was ushered out of harm's way.
The Whites pick up their sixth league win of the season, and increase their unbeaten run to nine in all competitions.
Salisbury's next game is at home to Eastbourne Borough in the FA Cup 4th Qualifying Round as they look to win a place in the first round.
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