The Phoenix had to claim all three points and rely on other round 25 results to have any hope of finishing in the top six.
Kazuki Nagasawa's matchwinning header in the 56th minute lifted Wellington to seventh on 33 points, behind Melbourne City (35) and ahead of Macarthur FC (31).
But Saturday's game at Christchurch's Apollo Projects Stadium marked a new low for Western Sydney.
"It's a first wooden spoon that I think the club's been a part of and we're all a part of it - everyone plays a part of it, the players, the staff, the club," stand-in skipper Brandon Borrello told Sky Sports NZ.
When asked how the Wanderers finish the season on a high against Melbourne Victory next Saturday, Borrello said: "Pride. As football players we're all winners and we've not done that all season and now we're in the spot where we are.
"So whether you're playing for a contract or playing for the next coach to try and get a spot, this is livelihood and we've got to show a bit of pride and a bit of hunger and it's not been enough from everyone across the board.
"You've just got to hold the mirror up. Everyone's played a part in why we're in this position, good or bad and I think a bit of self reflection is always good - whether it's a hard chat with yourself or a bit of constructive criticism."
City play lowly Brisbane on Saturday evening and can yet end the Phoenix's season.
"We spoke about it earlier in the week that we wanted to control our destiny and if other teams were gonna control our destiny, they'd need to work really hard to take it off us," interim boss Chris Greenacre said.
Wanderers interim coach Gary van Egmond, in his penultimate game at the helm before Ufuk Talay takes over, dropped captain and goalkeeper Lawrence Thomas, calling upon Jordan Holmes.
Wellington drew first blood in the 16th minute when Payne hung a dangerous ball up at the back post and Ifeanyi Eze headed home.
The visitors equalised after some quick thinking at a short corner.
Angus Thurgate worked the ball to Borrello - criminally left unmarked - and the Socceroo drove home.
The Phoenix's winner arrived when Payne floated a wonderful ball towards the near post and Nagasawa scored with an unstoppable header.
Wellington held on for dear life late, with Joshua Oluwayemi brilliantly denying Bozhidar Kraev at the death to preserve the victory.
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