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The seventh-placed side scored two first-half goals from corners. David Ball tapped in at the far post in the 24th minute for his fifth goal of the season after pouncing on a loose ball in front of goal.
Keanu Baccus levelled the game for the Wanderers five minutes later before Israel's Tomer Hemed put Wellington in front again in the 42nd minute. Clayton Lewis found Hemed free in the box from the corner as he scored in ninth goal in 12 games.
The Wanderers had a final onslaught in the closing minute of the game with defender Tim Payne making a crucial block on goal to deny the home side an equaliser in injury time.
Ufuk Talay's side now sit two points behind both Macarthur FC and Central Coast Mariners, but have played one extra game.
The Phoenix head back across the Tasman to host eight-placed Perth Glory at Eden Park on Sunday with a win needed to jump into the top six.
There will be concerns over the fitness of young Phoenix star Reno Piscopo who left the field inside the opening 10 minutes with a shoulder injury.