Red Rewind: Lambs chopped down by City
A couple of quality goals from Paul Groves and Paul Robinson were enough as the hosts won for the first time in seven months - their previous triumph coming at the expense of Carlisle United in January.
The Minstermen had begun non-league life with a deflating 2-0 defeat at Aldershot Town, which included the sending-off of new midfielder Gary Pearson. But they were to waste precious little time against their next challengers.
Player-manager Chris Brass and former Newcastle United striker Robinson soon linked up on fifteen minutes to allow veteran midfielder Groves to spectacularly rifle into the top corner from the edge of the area.
Groves then glanced a near post header narrowly wide from a Darren Dunning corner delivery before Tristram Whitman failed to take advantage of Chris Clarke's error at the other end.
Lambs striker Neil Ross also shot wide after the break from a quickly-taken free-kick, with both Groves and Steve Davis replying too high.
But with an hour played City extended their lead in fine style, Robinson producing a superb finish past Ryan Price after Brass' sweeping pass released Andy Bishop.
Tamworth had a later effort disallowed, while there were also a couple of scrambles inside the home area - although their opponents were always well-deserved winners on the night.
York City: Crichton, Law, Davis, Clarke, Smith, Brass (Arthur 90), Groves, Dunning, Stewart, Robinson, Bishop (Yalcin 86)
subs (unused): Porter, Merris, Nogan
Goals: Groves (15), Robinson (60)
Tamworth: Price, Johnson (Shaw 80), Smith, Brown, Sheppard (May 68), Ebdon, Cooper, Stamps, Blunt, Ross, Whitman
subs (unused): Bampton, Smith, Turner
Ref: P. Canadine (South Yorkshire)
Video Link: YorkCityTV