Veteran striker Iyseden Christie scored a penalty for Tamworth as Darlington lost for the first time this season.
The visitors had threatened early on but striker Ryan Bowman saw his close-range effort saved by Jonathan Hedge.
Tamworth came close twice when first Kyle Patterson had a volley parried away and then Danny Mills saw his shot saved after half-time.
The game looked to be heading for a draw until Ben Purkiss fouled Patterson in the box and Christie slotted home.
Tamworth: Hedge, Tait, Barrow, Francino Francis, Green, Cain (Jay Smith 85), McDonald, Bradley, Patterson, Mills (Thomas 65), Shariff (Iyseden Christie 58). Subs Not Used: Collister, St Aimie.
Darlington: Russell, Purkiss, Greg Taylor, Lee, Miller, Atkinson, Chandler (McReady 61), Kris Taylor, Ryan Bowman (Bridge-Wilkinson 38), Hatch (Smith 70), Walshaw. Subs Not Used: Pocklington, Campbell.
Booked: Lee, Walshaw, Purkiss.
Ref: Jeremy Simpson (Lancashire)