A game of two halves – with Vale poor in the first-half and desperately unlucky in the second – saw them lose their unbeaten record.
Vale named an unchanged side but included Byron Moore on the bench.
However, the visitors took a surprise but deserved early lead when Gary Jones scored after just eleven minutes.
Vale were not performing at their recent high standards and were guilty of too much sloppy play.
The visitors nearly doubled their lead but Duffy cleared off the line.
It was 0-1 at half-time after probably the worst 45 minutes of the season.
Several minutes into the second-half, poor defending nearly allowed County to double their lead only for Sam Johnson to rescue Vale.
Vale made changes including the introduction of Byron Moore to a deserved standing ovation and it paid as the side started to raise their game.
A melee saw several Vale players having efforts cleared and then Moore had a decent chance as Vale pressed.
With fifteen minutes left, Vale had two efforts cleared off the line as they did everything but score.
As Vale pushed even more, Marshall went desperately close as Vale, who had won over a dozen corners, did everything but score. Then Pope’s effort hit Daniel on the line as Vale went close again.
With five minutes left, County delivered a sucker punch as Liam Noble hit a deflected free-kick past Johnson.
Micky Adams and his players will reflect on what could have been and how they can sustain their second-half form and not repeat their first-half performance.
Vale: Johnson, Veseli (Dodds), Duffy, McGivern, Dickinson, Birchall (Moore), O’Connor, Lines, Marshall, Pope, Williamson (Daniel)
Subs: Neal, Jennings, Robertson, Brown
Attendance: 5,090 (391 away)