Newport took the lead through Chris Zebroski's fine half-volley from 20 yards after 16 minutes and Michael Flynn's penalty doubled the advantage shortly after the break.
But the Dons hit back quickly when George Francomb's free-kick was deflected in by Kwesi Appiah before Francomb himself levelled up the scores with a deflected strike after 69 minutes
The draw moved the Dons up to 53 points and though they remain one place behind Newport with little left to play for in mid-table, boss Ardley has issued his players with a challenge.
"I want to finish the season strong now. I've challenged my players to do what no one at this club has done before," said Ardley.
"We want to finish with 60 points so the fans can look at it and say we may have had our ups and downs, but look where we've ended up.
"We've got two and a half weeks left now before a six-week break and we'll go as hard as we can go.
"It's a good point after the way we played in the first half and from being 2-0 down. We should never have been there after the way we played in the first half. I thought we could have been 3-0 down at half-time.
"But we have got a bunch of players who have got a bit of character about them.
"As much as we'd like to score the first goal we fought back well."