Super-sub Ibini sealed Saturday's 2-1 upset win in the 97th minute on a Sydney afternoon so hot that the day's earlier match - between Western Sydney and Melbourne Victory - was postponed.
Storming into the box from the left wing, Ibini combined with Abbey Lemon on a clever one-two before curling her strike past Phoenix goalkeeper Carolina Vilao.
"It feels great. I think it was a long time coming," said Lemon.
"We've been so close for so long and I'm just happy we could do it today in front of a home crowd.
"It feels amazing. I mean they come week in, week out, whether we win lose or draw and I really wanted to get the three points again today for all of the fans that keep coming back and supporting us."
With four more rounds remaining before finals, Wellington blew a golden chance to move into the top six to finish the weekend after dominating possession.
Instead, they will sit in eighth place at the end of round 19, two competition points behind sixth-placed Central Coast.
The Sky Blues, meanwhile, scored a fourth win at Leichhardt Oval this season to push local rivals Western Sydney to the foot of the table.
In only her second ALW game, Sydney goalkeeper Jasmine Black was immense.
She finished her first start with eight saves, two of those coming in quick succession early on as Manaia Elliott had two good looks.
Sydney's Maddie Caspers celebrated her 18th birthday with a goal against the run of play in first-half added time, nudging into the net after defender Tiana Jaber lost her footing.
It was an afternoon to forget for Jaber, who was shown a second yellow card for a challenge on Shea Connors in the final five minutes of regulation time.
The misstep reduced the Phoenix to 10 players as they hunted victory, after an unmarked Elliott made good on a Annalie Longo cross to equalise in the 75th minute.
Instead, it was Ibini who stood up as Sydney confirmed a second win from three starts.
28°C