Phoenix scored three first-half goals in 17 minutes, with striker Roy Krishna bagging a brace, to help Wellington coach and former Sydney FC captain Mark Rudan enjoy a memorable win over his old club.
Defender Michael Zullo pulled a goal back in the 89th minute but Sydney suffered their first successive home loss since April 2016.
It was Wellington's first win over Sydney in seven games and they had picked up just one point in their previous eight away games against all comers.
Sydney's defence was caught ball watching in a nightmarish first-half as a series of passes and crosses cut them apart.
Krishna raced on to a perfect through-ball from Sarpreet Signh in the 21st minute and outpaced Michael Zullo and Jop Van der Linden before slotting it past Sydney goalkeeper Andrew Redmayne.
He scored again seven minutes later when he ran on to a Mandi through-ball, shook off Zullo and netted.
Central defender Steven Taylor completed Phoenix's first-half blitz when he got in ahead of van der Linden to head home a Liberato Cacace cross in the 38th minute.
It might have been a different story had Sydney's normally efficient goalsneak Adam Le Fondre not squandered a golden opportunity in the 14th minute.
Le Fondre was off target from close range following a fine cross to the near post by Paulo Retre.
Sydney captain Alex Brosque came close just before halftime when his shot was hacked clear by Taylor, with Phoenix goalkeeper Oliver Sail off his line.
Sydney coach Steve Corica made a change at halftime replacing Retre with marquee Siem de Jong, the Dutchman playing for the first time in five rounds following a hamstring injury.
De Jong had a shot pushed away by Sail in the 57th minute and Phoenix survived some penalty area scrambles and VAR reviews before Zullo's consolation goal.