Goal-scorers Michael Wylde and Craig Reid battle for the ball
A second-half Craig Reid penalty secured Newport County their first point at Conference level in 21 years.
Tamworth, top of the table after their 4-2 opening win over Eastbourne, were ahead after just three minutes.
County were unable to clear a corner effectively, Danny Thomas played the ball back into the box and Michael Wylde glanced in the header.
Newport struggled until Sam Foley burst into the box and was felled by Richard Tait, Reid blasting in from the spot.
Alex Rodman nearly snatched the win for the Lambs late on, but Glyn Thompson showed a safe pair of hands to send the 2,217 Spytty Park crowd home happy.
Newport County manager Dean Holdsworth: "It's disappointing, but I'm delighted with the second-half performance.
"There wasn't a lot in the first half - a set piece cost us the goal - and in the second half we were absolutely outstanding.
"We've shown what we can do with the ball, but we can't switch off at set pieces.
"It's a learning curve for us. We created five or six chances but the goalie pulled off some great saves and it was not to be.
"We'll build from this. We'll learn quickly. I believe in this team."
Newport County: Thompson, Bignot, Collins, Warren, Odhiambo, Todd, Rose, Henry (Rogers 82), Sole (Matthews 46), Reid, Foley. Subs Not Used: Garner, Thorne, Knights.
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