The Phoenix remain in 10th position and five points behind sixth-placed Macarthur.
Wellington centre-back Isaac Hughes was unmarked and headed home in the 61st minute after a trademark curling corner by Hideki Ishige.
Roar captain Jay O'Shea hit the inside of the left post minutes later with a super strike that rebounded across the face of goal as the visitors refused to relent.
Two of the Roar's best attacking talents combined to draw level in the 72nd minute. Keegan Jelacic came off the bench to thread a sublime pass through for Henry Hore, who mesmerised the Phoenix defence before scoring his 16th ALM goal.
Both sides produced late bursts but were unable to score.
The Phoenix have won just one of their five previous games and none of their previous three at home.
The only points the Roar have picked up this season are on the road, with two draws and a solitary win over Sydney FC.
The Roar started full of running. Ben Halloran had an early shot blocked after good lead-up from Samuel Klein. Klein then had a great chance in the eighth minute after a cross by Louis Zabala, but headed over the bar.
An errant Roar back pass almost gifted striker Kosta Barbarouses a goal, but his shot was saved by Macklin Freke.
A magnificent strike by Ishige across his body and while at full pace after a cross from the right by Corban Piper was disallowed by VAR. Ishige was offside by a toe and just ahead of Roar defender Walid Shour.
The VAR decision was mulled over for three minutes with the final call of no-goal displeasing the Wellington faithful, who made up most of the 9084 fans.
The hosts upped the ante before half-time with Piper and Ishige dangerous.
Referee Jack Morgan was called on by VAR again when Ishige was brought down by Shour in the box, but no penalty was awarded as the sides went in to half-time with nothing to show on the scoreboard.
Veteran Tim Payne came off the bench for Wellington after a month out with a foot injury and almost provided Barbarouses with a late winner with a class cross.
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