Bottom-placed Forest Green are still without a point this season and have now conceded 14 goals in four games.
Tristram Whitman put the hosts ahead with a right-foot strike into the bottom corner after 19 minutes.
Tamworth's pressure yielded another goal early in the second-half, Marcus Ebdon drilling the ball home.
Neil Ross effectively secured victory in the 52nd minute when he shot low to Perrin's right, and Whitman poking the ball home to complete the rout.
Tamworth: Price, Adie Smith, Redmile, Brown, Stamps, Ebdon (Bampton 79), Cooper, Sheppard, Colkin (Shaw 67), Ross (May 63), Whitman. Subs Not Used: Nick Smith, Johnson.
Booked: Ross, Cooper.
Goals: Whitman 19, Ebdon 46, Ross 52, Whitman 73. Forest Green: Perrin, Gould (Green 57), Gadsby, Richardson, Betts, Cowe, Rushbury (Rogers 61), Hodgeson, Sykes, Beesley, Griffin (Danks 59). Subs Not Used: Cleverley, Greaves.
Ref: S Rubery (Ilford).