Reeeling from back-to-back losses to Auckland FC and Newcastle, the Phoenix were seeking a response - and delivered.
Wellington lost goalkeeper Josh Oluwayemi just 10 minutes into the game after he landed awkwardly and was substituted with a right leg injury.
Eamonn McCarron came on for his A-League Men debut and watched on as teammate Corban Piper opened the scoring in the 36th minute.
Sabit Ngor equalised in first-half added time but the Phoenix scored twice in four minutes early in the second half to seal victory.
"It's nice to get a win before Christmas," skipper Alex Rufer told Sky Sports NZ.
"We've worked really hard and happy to get the three points.
"... There's been a lot of noise. We've been disappointed with how we've been going, both in performing and in the results. So today was all about getting three points."
Both teams spurned good chances in an action-packed opening half hour.
Then, Kazuki Nagasawa proved the architect of Central Coast's undoing.Â
The Japanese attacker intercepted a stray pass, drove through midfield and slipped through Piper, who coolly finished past Andrew Redmayne.
Central Coast hit back with one of the final plays of the half.
Miguel Di Pizio stung the palms of McCarron with a fierce strike and the young goalkeeper could only parry the ball to the back post, where Ngor was on hand to tap home.
Two minutes into the second half, Wellington received a penalty, following a VAR review, after Will Kennedy handballed Ramy Najjarine's attempted cross.
There was nothing Redmayne could do about Manjrekar James's fierce spot kick that restored the hosts' lead in the 49th minute.
Three minutes later, Carlo Armiento finished off a superb team move to make it 3-1.
The Mariners' defence were unable to clear a Matthew Sheridan cross and Piper pounced, sending the ball across the face of goal for Armiento to drill home at the back post.
"Came out second half slow and we got punished by them. Credit to them," Mariners skipper Bradley Tapp told Sky Sports NZ.
"We've had a tough run, bad results but the only thing we can do now is stick togther - we can't tear each other apart. So we'll pick ourselves up next week."
Wellington next travel to face Melbourne Victory on December 29, while the Central Coast are back in action against Brisbane on New Year's Eve.
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