Farnham's fully committed team performance was too much for a competitive Chessington side on Tuesday night.
An end-to-end game was played at a furious pace and Town had some narrow escapes before scoring the all-important first goal after 33 minutes.
Jason Blake's punch put the 'keeper under pressure and his poor punch fell to Alan Morgan who headed into an empty net.
Morgan was on target again when Farnham added an equally important second goal on the stroke of half-time.
Graeme Miles cut inside his defender on the left and delivered a fine cross for Morgan to show his heading ability: 2-0 at the interval.
After some close misses at both ends, Farnham wrapped the game up in the 63rd minute. Paul Hatton, making his first appearance of the season, played in a teasing cross from the right and Moore nipped in to score with a looping header. Besant pulled one back for Chessington and missed an easier chance to make it 3-2.