The Mariners headed into Friday's game in Gosford on the back of three successive defeats, but led at the break through Bernie Ibini-Isei's 20th-minute strike.
Wellington then turned the game on its head in the second half, with Kenny Cunningham, Carlos Hernandez., Stein Huysegems and substitute Jeremy Brockie all finding the net.
Things could have been different had Mile Sterjovski converted a penalty for Central Coast with the score at 1-1, but the former Australia international was denied by Glen Moss and the visitors duly took advantage by romping to a victory that moves them up to sixth.
Ibini-Isei opened the scoring following good work from home debutant Kim Seung-Young, only for Wellington to level two minutes after the interval as Cunningham drove home Reece Caira's deflected cross.
Seven minutes later a bizarre scenario saw Phoenix captain Andrew Durante handle the ball in his own area, when it appeared he was attempting to grab the ball in anticipation of his own side receiving a free-kick.
Sterjovski stepped up to take the resulting penalty, but Moss dived to his right to deny the midfielder and keep the score level.
Wellington went on to score in the 64th and 65th minutes, Hernandez firing home via the underside of the crossbar before Huysegems capitalised on Cunningham's header across goal to grab his 10th goal of the season.
With eight minutes remaining, Huysegems set up Brockie for a fourth away goal that sealed an emphatic win.
