An early Carlos Hernandez strike was cancelled out by a Craig Goodwin goal after 25 minutes before Stein Huysegems gave the visitors a 2-1 lead at half-time.
Goodwin's second goal early in the second half levelled the score before substitute Jason Hicks grabbed the winner with a well-taken strike in the 71st minute.
The win sees the Phoenix move into the top six while the Jets remain in second-last place and in danger of falling out of finals contention.
The Phoenix started the match with purpose, engineering a shot on target for Tyler Boyd after just 10 seconds of play before Huysegems set up Hernadez for a pile-driver that forced a stinging save from jets goal-keeper Mark Birighitti.
After weathering the early storm the Jets created a few chances of their own. Adam Taggart was played in for a one on one with Wellington custodian Glen Moss who he rounded but was unable to cut the ball back for Goodwin, who was unmarked in front of an open net.
Goodwin had a chance moments later when he showed a sparkling turn of pace to get outside the defence before cutting back and firing a shot that sailed over the crossbar.
The visitors opened the scoring on the 20-minute mark when the Newcastle defence allowed Hernandez too much time and space on the edge of the area and the Costa Rican took the opportunity to rifle a low shot inside the near post for a 1-0 lead.
The home side were forced into an early substitution when make-shift striker Nick Ward succumbed to a knee injury and was replaced by Joey Gibbs after 23 minutes.
Just two minutes later Newcastle equalised when Zenon Caravella did well to beat two defenders before sliding a ball into the box where Goodwin smacked a first-time strike into near top corner.
Wellington went back in front when Hernandez was again allowed too much time on the ball and he fed a lovely pass for Huysegems, who did well to thread his shot into the corner of the net.
There was more drama right on the stroke of half-time when the Jets had a penalty claim turned down when it looked as if Phoenix defender Josh Brindell-Smith handballed in the area, but it was waved away and Wellington went into the break with their noses in front.
The Jets equalised just after the interval via a lovely solo effort from Goodwin. He got the ball on the left-wing and weaved between two players to race inside the box and then fire a shot across Moss and inside the far post.
Wellington regained the lead midway through the second half when a contested ball fell to Hernandez in space and he slid a ball across for substitute Hicks who did well to wrong foot the Jets defence before curling a 15-metre effort inside the far post.
Newcastle Jets 2 (Goodwin 26, 46)
Wellington Phoenix 3 (Hernandez 21, Huysegems 33, Hicks 71)
Crowd 10,406 @ Hunter Stadium
