Goals from Lloyd Blackman and Sasha Opinel earned Farnborough victory.
The visitors took an early lead through Blackman's close range finish, and only a great save from Ryan Prince stopped Gary Holloway from making it two.
While Tamworth were struggling to create any chances, Farnborough went close again in the second-half when Tony Taggart's header hit the bar.
Boro made the points safe when Opinel fired home a free-kick after Lee Colkin had fouled Danny Allen-Page.
Tamworth: Price, Adie Smith (Taylor 68), Redmile, Brown, Stamps, Blunt (Shaw 78), Cooper, Bampton, Colkin, Ross, Whitman.
Subs Not Used: Storer, Johnson, Sheppard.
Booked: Cooper, Taylor, Colkin, Redmile.
Farnborough: Craig Holloway, Townsend, Miles, Charles, Opinel, Taggart, Hughes, Gary Holloway, Allen-Page, Hamilton (Riddell 75), Blackman.
Subs Not Used: Osborn, Theo, Belaid, Mulhern.
Booked: Allen-Page, Hamilton.
Goals: Blackman 8, Opinel 77.
Ref: M Harris (Lincolnshire).