Bernie Ibini opened the scoring on 14 minutes before Shane Smeltz - who started in place of marquee man Marc Janko who didn't travel due to a thigh strain - netted from the penalty spot on 32 minutes to give the Sky Bues a 2-0 cushion at half-time.
A minute after the restart, Wellington hit back with defender Michael Boxall slotting home from close range to the delight of the majority of the 13,248 fans in attendance.
The win lifted Sydney level on 50 points with league leader Melbourne Victory - but trailing by a goal difference of six - while the defeat resulted in Phoenix dropping to fourth behind Adelaide United on goal difference.
The Sky Blues get a week off while the elimination finals next week will see sixth-place Brisbane Roar facing the Reds at Adelaide Oval on Friday night and Wellington host fifth-place Melbourne City at Westpac Stadium next Sunday.
Heading in to the finals series, Sydney coach Graham Arnold may well have to do without young attacker Chris Naumoff who suffered an arm injury and was replaced before the break.
Sydney was undeterred by the late withdrawal of golden boot leader Janko, with the pace of Ibini and Naumoff dominating the midfield.
Skipper Alex Brosque and Smeltz also impressed and provided plenty of options in the front third.
Phoenix again spurned a gilt-edged early chance when referee Strebre Delovski pointed to the spot after Ibini clipped Michael McGlinchey after just 10 minutes.
Roly Bonevacia stepped up to the spot but skewed his shot wide, with Ibini making Wellington pay minutes later.
Set loose on a storming run down the left by a fine throw from goalkeeper Vedran Janjetovic, the pacey striker turned Boxall inside out before slamming the ball home.
Ex-Phoenix favourite Smeltz doubled Sydney's lead, stepping up to the spot and coolly converting a penalty after Albert Reira brought down Naumoff.
Wellington halved the deficit barely a minute into the second half, working a smooth variation to score for the first time all season off a corner.
The decision to go short worked a treat with Burns hauling back a cross for Boxall's poised finish, which galvanised the passionate home support.
Brosque almost silenced them in the 63rd minute when he broke clear to confront Lewis Italiano one-on-one.
But the stand-in keeper stood strong and made a point-blank save.
Wellington pushed hard right to the final whistle but couldn't repeat the heroics of the previous week's stoppage-time winner against Central Coast Mariners.
The final game of the campaign sees Victory take on Central Coast Mariners at AAMI Park with the Premiers' Plate all but locked away.