Rock-bottom Leigh claimed their third win of the season with a Gary Williams goal on the hour mark before holding out with a strong defensive display. Farnborough missed a good chance to secure an early breakthrough when Robert Traynor sent his close-range shot wide of the post.
Leigh's Warren Peyton also missed the target before the break.
Williams fired home after connecting with a Chris Sim pass before the hosts threw everything forward in response.
Farnborough: Osborn, Adam Theo, Burton, Miles (Deane 70), Rooney, Turner, Holloway, Canham (Johnson 75), Bernard, Traynor, Braley (Mulhern 64). Subs Not Used: Jean-Zepherin, Allen-Page.
Leigh RMI: Worsnop, Lane, Chris Clarke, Roscoe, Peyton, Shillito, Stoker (Ryder 82), Peers, Ryan Clarke, Walsh (Simm 29), Williams (Taylor 75). Subs Not Used: Turner, Byrne.
Booked: Peyton.
Goals: Williams 60.
Att: 501
Ref: R Shoebridge (Derbyshire).