A clinical first-half double from Noah Botic - scored from his team's only two shots - and a header after the break from Tongo Doumbia allowed United to climb out of last place on the ladder.
They had clung on for their lives in the first half, needing a string of saves from Jamie Young to keep them in front after Beka Mikeltadze gave the Jets a 33rd-minute lifeline from the spot.
But they took over late and sealed their first win in five games, at the same time ending the Jets' six-game unbeaten run and costing them an opportunity to jump into the top six.
The win meant they ended Saturday 10th on the table, only five points off the top six, despite their recent poor run.
"We want to make play-offs," Troisi told Paramount.
"If we're not consistent, we won't do that ... that's our aim, we got a good foundation today.
"You see when we do the right things and create chances we can score goals and we're a good side.
"Everyone's written us off and the only way we can turn it around is to put on performances like this."
Botic was perfectly positioned twice in the opening half-hour, ducking in to nod Josh Risdon's cross home early before tapping home another peach from Connor Pain.
Mikeltadze got the Jets on the board, easily tucking home his penalty after a Jacob Tratt handball gifted Newcastle a lifeline.
But the hosts spurned a number of chances to equalise throughout the first half and just when it looked like they might grab one in the second, Doumbia put things to bed with a back-post header - his first goal for United.
Newcastle looked particularly brittle at the back throughout and were almost caught out a number of times by careless passing, one back-pass missed by goalkeeper Jack Duncan rolling narrowly wide.
The experienced Troisi praised Botic's precision in front of goal.
"He's a good young talent, he works hard. In our team he's going to get a lot of chances because we create a lot," he said.
"He probably could have had another one or two ... we'll keep feeding him and doing as much as we can so he can thrive."
Newcastle could have gone fourth with the win but instead remain seventh, although they were not overly punished in the race for finals thanks to sixth-placed Sydney's loss to Melbourne City.
"I don't think we defended the box really well - it was three crosses, three goals," Jets midfielder Angus Thurgate told Paramount.
"We could have been more clinical, especially in that first half, we had a few chances to get a goal and we didn't.
"It's a tight competition this year. We know we're in the mix ... but we need to defend better."
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