Chris Morgan was the matchwinner for Newry with a glancing header from an Ian Curran cross after 56 minutes.
Portadown took a seventh minute lead when Andy Smith got a close range touch on Kevin Braniff's shot and then Aime Koudou and Wesley Boyle had chances.
Newry equalised two minutes before the interval when Stephen Garrett met Kevin Keegan's ball with a glancing header.
Portadown stay fifth and Newry seventh in the league with one set of fixtures to play.
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