Needing three points to leapfrog Melbourne Victory at the summit, Ernie Merrick's men squandered a host of chances, headlined by a first half penalty miss from Socceroos star Nathan Burns.
But the Phoenix didn't have it all its own way and had keeper Glen Moss to thank for a string of saves as City went for the jugular in the second half.
Though already assured of a top-six finish thanks to the expulsion of Perth Glory from the finals, sixth-placed City showed no signs of complacency as it roared out of the blocks with Jonatan Germano and Robbie Koren firing off early efforts on goal to test Phoenix keeper Glen Moss.
Phoenix wasted a glorious chance to take a 14th minute lead when Burns fluffed his lines from the penalty spot with his tamely hit effort aimed straight at grateful goalkeeper Tando Velaphi after Louis Fenton had been shoved over by Sinagaporean Safuwan Baharudin.
Defender Manny Muscat then wasted an inviting opening as he burst into the box, only to place his shot far too close to Velaphi.
Another opportunity went begging for the visitor in the 33rd minute when Fenton raced down the right and crossed for Roy Krishna who blasted his shot just wide of Velaphi's left hand post.
Wellington picked up from where it left off in the second half with Burns lashing a 54th minute shot which was tipped over by Velaphi.
At the other end two minutes later Aaron Mooy fed Josh Kennedy and the former Socceroos striker's left-footed shot was tipped away by the diving Moss.
The Phoenix goal was under threat again in the 69th minute with a flowing move ending with Koren forcing Moss into a fine save at his near post.
Moss came to the rescue again in the 80th minute, turning aside Germano's stinging shot after he had been released by Mooy's first-time pass.
City midfielder Erik Paartalu almost found a late winner when his injury-time header rocked the crossbar.
Coach John van 't Schip said the match, City's fifth without defeat, was "full-on".
"I didn't have a second to sit back," he said. "The confidence in the team has grown a big deal. All in all, the result was maybe a fair result."
Phoenix boss Ernie Merrick said aside from Burns' penalty, which he called "the worst penalty in the world", he was happy to take the point after two straight 3-0 home defeats.
"We got our passing game going, our midfield going," he said. "I think we created more better chances ... but we're pretty happy."
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