Bath remain without a win this season as they lost at home against Tamworth.
Goals from Danny Thomas and Nabil Shariff gave The Lambs victory and moved them up to fifth in the table.
Thomas fired Tamworth into the lead with a well-struck shot from 30 yards and the visitors nearly doubled their lead but Kyle Patterson headed over.
Adam Connolly missed a header and Lee Phillips shot wide for Bath before Shariff sealed the win late on when he shot high into the net from six yards.
Bath City: Garner, Simpson, Preece (Canham 65), Jones, Stonehouse, Russell (Egan 76), Connolly, Burnell, Hogg, Cook (Murray 58), Phillips. Subs Not Used: Mills, Rollo.
Tamworth: Hedge, Tait, Francino Francis, Green, Bradley, Jay Smith, Barrow, Thomas, Patterson (Shariff 73), Mills (Cain 66), Iyseden Christie (St Aimie 89). Subs Not Used: McDonald, Reynolds.
Booked: Bradley, Jay Smith.
Goals: Thomas 31, Shariff 90.
Ref: Justin Amey (Dorset)