Two penalties conceded by York defender Chris Smith gifted a fortunate victory to Tamworth.
Chances were sparse in the first half, although Tamworth goalkeeper Jonathan Hedge tipped over brilliantly to deny Ashley Chambers.
Smith fouled Kieran St Aimie who picked himself up the convert the penalty.
Danny Thomas was then fouled by Smith, with substitute Iyseden Christie slotting home the spot kick, before Jason Walker headed a consolation.
Tamworth: Hedge,Tait,Francino Francis,Green,Habergham, Patterson (Thomas 28),Smith,Bradley,Mills (Iyseden Christie 67), St Aimie,Shariff (Cain 83).
Subs Not Used: Valentim,Collister.
Booked: St Aimie.
Goals: St Aimie 53 pen,Iyseden Christie 73 pen.
York: Ingham,Oyebanjo,Smith,McGurk,Meredith, Challinor (Henderson 66),Kerr,Moke (Reed 46), Blair (McLaughlin 54),Walker,Chambers.
Subs Not Used: Parslow,Boucaud.
Goals: Walker 84.
Ref: Graham Horwood (Bedfordshire).