The Jets started Sunday's match full of fire, with Lachlan Rose striking first in the 18th minute before Kota Mizunuma doubled the lead four minutes later.
At that point, Sydney were sitting seventh on the live ladder - two points adrift of sixth spot.
Goals to Douglas Costa and Adrian Segecic levelled things up by the 55th minute, and Jaiden Kucharski scored what turned out to be the winner in the 83rd minute.
The result lifted Sydney into sixth spot with tough away games against third-placed Western United and second-placed Melbourne City to round out the regular season.
Sydney entered Sunday's match looking to put the disappointment of their ACL Champions League Two semi-final exit behind them.
Sky Blues marquee player Costa was crucial in the win, with his creativity and smarts causing Newcastle's defence all sorts of problems.
"It's a massive win," Sydney coach Ufuk Talay told Paramount.
"Everything's in our hand to play finals football this season.
"The boys probably started the game slowly, but after 25, 30 minutes we started to control the game and got the goals we needed for the three points."
Controversy surrounded Newcastle's opening goal, scored from close range by Rose in the 18th minute.
Sydney players were adamant the heels of Jordan Courtney-Perkins had been clipped by Newcastle's Elil Adams in the lead up to the goal, but VAR allowed it to stand.
There was no doubt about Newcastle's second in the 22nd minute, with Clayton Taylor's cut back across the face of goal finding Mizunuma, who ran onto the ball and fired home from the back post.
At 2-0 up, Newcastle were well on track to defeat Sydney at Allianz Stadium for the first time since 2012.
But star Sky Blues recruit Costa was having none of it, unleashing a beautiful drive from 22 yards out to peg a goal back for the home side in the 36th minute.
Scores were level in the 55th minute when Segecic continued his hot form with a strike from just inside the box.
And there was one more joyous moment for Sydney when Kucharski found himself in the right place at the right time to rifle his angled shot home.
The result officially ended Newcastle's faint finals hopes.
"I think today was an example of how far we've come as a group, but also how far we need to go as a club if we want to progress forward," departing Jets coach Rob Stanton said.
"I'm proud of the players. I think they've delivered a brand and identity that's clear to everyone.;
"A little bit fearless, lacks a little bit of experience and leadership at times. But the leaders are growing, and the future looks bright."
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