Ronnie Moore’s side had climbed out of the bottom two thanks to four straight wins, and they had looked on course to make it five when a Lee Minshull own goal and Jordan Hugill’s first strike for the club put them in control.
But County skipper Darren Jones pulled one back just before the interval, with Aaron O’Connor’s 11th goal of the season securing a share of the spoils.
Pools took the lead in the 15th minute when midfielder Minshull’s attempt to cut out Michael Duckworth’s cross ended with him heading the ball into his own net.
The visitors doubled their advantage in the 38th minute when the lively Jonathan Franks hit the bar from distance, and on-loan Preston forward Hugill bundled in the follow-up.
Play-off chasing Newport needed a response and they got one three minutes later when centre-back Jones dispatched a fierce low strike into the back of the net from Max Porter’s lay-off.
O’Connor then slid home the equaliser just two minutes into the second half before Scott Flinders’ save denied County’s David Tutonda a late winner.