The first half was more notable for rain than chances raining down on goal.
Mike Carvill made the breakthrough for Wrexham after the break by rounding Newport goalkeeper Mark Ovendale.
But the home side hit back swiftly to take the lead within five minutes, first Jason Bowen converting a penalty before Craig Hughes rose highest to thunder home a Steve Jenkins cross.
The New Saints have already won through to the final of the competition by knocking Cardiff out at the semi-final stage the previous night.
That means for the first time in the FAW Premier Cup's history, none of the 'big three' of the Nationwide League clubs - Cardiff, Swansea and Wrexham - will contest the final.
Chances were hard to fashion at a wind-swept Spytty Park in a low quality first half.
Former Charlton Athletic striker Carvill's effort on target was the closest that Wrexham came to breaking the deadlock.
Newport fared little better, with a shot into the side netting just before half-time from Bowen the best the home side from Conference League South could muster.
Things warmed up after the break, as Carvill broke through the Newport rearguard on 51 minutes to convert a one-on-one against goalkeeper Ovendale.
But within two minutes the home side were level, Charlie Griffin sent tumbling in the Wrexham area to earn a penalty that Bowen stepped up to stroke cooly home.
Newport wasted no time in grabbing a second to take the lead on 56 minutes.
Bowen was again involved as he combined down the right flank with Steve Jenkins, whose cross was headed home by Hughes.
Hughes and Bowen both had good chances to make County's lead safe and they should have been made to pay.
But Wrexham striker Lee McEvilly mis-kicked with the goal at his mercy to waste a golden chance to send the tie into extra time.
The Dragons now have just their League Two relegation struggle left to occupy them this season.
BBC