County are having somewhat of an inconsistent start to the campaign after losing 1-0 to Oxford United last week. It was back to winning ways here, however, while York are now without a win in six.
James Loveridge looked lively for the hosts but was kept at bay by York and could only test Ingham from distance.
It didn't take long for County to make use of their numerical advantage when, in the 52nd minute, Andrew Hughes's fine shot found its way in off the post.
Newport sensed victory was in their grasp against their faltering opponents and should have been ahead in the 59th minute when the ball hit everything but the York net after a goalmouth scramble.
The hosts' perseverance finally paid off on the 65th minute when Chris Zebroski rounded the goalkeeper and slotted into an empty net.
The turnaround was complete four minutes later when Darren Jones scored his second screamer of the season for the hosts, firing the ball into the top corner.