County battled to a 1-1 draw, as Offrande Zanzala's second-half penalty earned a point on the road.
After a first half that went by without much in the way of shots on goal, Wimbledon took the lead through Ethan Chislett's free-kick.
A 67th-minute red card for Dons forward Kyle Hudlin allowed Newport back into the game though and three minutes later Zanzala's spot-kick made matters level.
County pushed for the winner but the 10 men of Wimbledon held on for a point in our first-ever visit to the new Plough Lane.
The game took a while to get going though, with County having the first half-chance as Priestley Farquharson headed Declan Drysdale's cross from the right wide.
Much of the first half did pass without goal-mouth incident though, although County did come close to breaking the deadlock in the closing stages of the opening period.
After a Mickey Demetriou long throw-in was headed out, Demetriou headed the ball back towards danger.
With both Zanzala and then Will Evans causing pressure in the area to force home, Wimbledon somehow scrambled clear as the ball looked goal-bound.
County then had another good opening in the dying embers of the first half, but Moriah-Welsh struck wide from the edge of the box after being set-up by a dangerous James Waite run.
Cameron Norman would have the first shot at goal in the second, but he struck wide of the far post three minutes after the restart.
Moriah-Welsh then had a powerful drive unconvingly pushed away by Wimbledon keeper Nik Tzanev but the Dons cleared their lines after Aaron Lewis picked out Zanzala who had his shot blocked.
Against the run of play, Wimbledon took the lead though through Chislett's impressive free-kick that he curled in from the left of the County box for 1-0.
That sparked the game into life and Wimbledon were reduced to 10 men in the 67th minute due to violent conduct from Hudlin.
Drama continued two minutes later when Moriah-Welsh was tripped in the box for a penalty which left Zanzala the task of slotting into the bottom right corner to make it 1-1 from the spot.
With a man advantage, County piled on the pressure as Drysdale headed Aaron Lewis' crossed free-kick from the right over the top.
Zanzala then almost got his and our second with an acrobatic attempt with the ball behind him after Evans headed Lewis' cross from the left back across goal - Zanzala diverted the ball over the bar.
AFC Wimbledon: Nik Tzanev, Alex Woodyard (C), Harry Pell, Josh Davison, Ayoub Assal (Nathan Young-Coombes '86), Ethan Chislett, Ryley Towler, Kyle Hudlin, Hus Biler, Jack Currie, Paul Kalambayi
Subs not used: Nathan Broome, Chris Gunter, Lee Brown, George Marsh, Alfie Bendle, Courtney Senior
Newport County: Joe Day, Priestley Farquharson, Declan Drysdale, Mickey Demetriou (C), Cameron Norman, Aaron Lewis, Scot Bennett, Nathan Moriah-Welsh, James Waite (Aaron Wildig '61), Will Evans (Omar Bogle '82), Offrande Zanzala
Subs not used: Nick Townsend, Matt Dolan, Robbie Willmott, Sam Bowen, Lewis Collins