Adam Cunnington's stoppage time penalty rescued a point for Tamworth to deny Newport at Rodney Parade.
Debutant Scott Donnelly gave Newport the perfect start when he pounced on a loose ball from close range to give his side the lead after 26 seconds.
Byron Anthony doubled the advantage on 30 minutes when he poked home from Lee Minshull's flick-on.
Lee Hendrie fired from the edge of the area to reduce the deficit before Cunnington's late penalty.
Cunnington scored from the spot in the third minute of stoppage time after referee Kevin Johnson adjudged Ismail Yakubu to have handled the ball.
VIEWS FROM THE DRESSING ROOM
Newport County manager Justin Edinburgh told BBC Radio Wales:
"The [penalty] decision's wrong. It's cost us two points. I spoke with the referee and he changed his description of the incident twice from when I confronted him on the pitch to when I've seen him in his dressing room. That tells me he doesn't know what he's seen and he's guessed.
"In terms of the performance it was a solid performance rather than spectacular, but without playing for three weeks I thought we did well. It was very unjust for us not to have taken three points today."