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City's six-match winning run was halted by Western United last time out, but it hit back at WIN Stadium to move to within two points of league-leader Central Coast Mariners with a game in hand.
Tomer Hemed equalised for Phoenix after Curtis Good had headed City in front from six yards, but Jamie Maclaren restored the visitor's lead with a powerful strike across Oliver Sail.
Wellington equalised for a second time before the hour through skipper Ulises Davila, who curled a delightful low shot into the bottom-left corner from 20 yards – the seventh goal they have scored from outside the box in the 2020-2021 A-League season.
Melbourne came away with the three points in Wollongong thanks to substitute Marco Tilio's late header after some good link-up play out on the right to make space for Connor Metcalfe's cross.
It was an early goal that proved the difference in the early kick-off between the Jets and Western United, with winger Wales slotting Dylan Pierias's through-ball into the bottom-left corner after just 36 seconds to make it goals in back-to-back games.
That was the first goal the visitor had scored in this fixture at the fourth attempt and was the earliest it has netted in its A-League history, putting it on course for a maiden victory against the Jets.
Craig Deans' sside attempted 20 shots in the remainder of the game, but just two of those were on target as they fell to a sixth loss in a row to remain second bottom of the division, while United are up to seventh with games in hand on the top six.