But the Jets were ahead 2-0 after only 18 minutes and Wellington struggled to convert the myriad chances they created during a frustrating spectacle.
Striker Roy Krishna got the home side on the board in the second spell and Wellington left it to the dying stages before Hicks curled his stunning strike inside the post.
"I thought it was a tremendous display of football without the finishing," Phoenix coach Ernie Merrick said.
Krishna and Nathan Burns were the worst offenders as they spurned multiple opportunities but Merrick continued his party line that he wasn't worried about the lack of finishing because they're still creating the chances, which is important.
"The boys are really dejected but I'm not. I've patted them on the back. Just because that final touch doesn't go in the goal, that doesn't mean we didn't play some terrific football."
Since the A-League resumed after the Asian Cup, the Phoenix have drawn two and lost two. They've collected only two competition points from a possible 12 recently against teams that are all below them on the ladder.
You can take it two ways: Firstly, that they're in crisis because they cannot win and they can't finish. Or you could note they're still in fourth place on the ladder and remain one of the league's highest-scoring sides.
Merrick, ever the optimist, doesn't seem bothered about the lull in form and believes his side will get back in the win column soon.
Yesterday's late flurry was a cruel way for the Jets to lose after they looked like they would pinch all three points at the temporary surrounds of the Hutt Recreation Ground.
They finished with 10 men after Ben Kantarovski was shown his second yellow card late in the game and coach Phil Stubbins wasn't pleased with how the contest was refereed by Kris Griffiths-Jones.
"I didn't want to say it but there's been a lot of people jumping on the referees of late and I think when he looks back on that he might think that he could have made a few better decisions there. Certainly there was nothing in there that helped us."
Merrick, who has expressed concerns about officials recently too, declined to offer an opinion.
Wellington Phoenix: 2 (Roy Krishna 68, Jason Hicks 90+4).
Newcastle Jets: 2 (Roly Bonevacia 12 own goal, Scott Neville 18). HT: 0-2.