The Sky Blues opened the scoring at McDonald Jones Stadium through Piero Quispe's 64th-minute goal, before a relentless Eli Adams made it 1-1 and sent Saturday night's game into extra time with a thunderous strike.
When neither side could find a match-winner, Sydney goalkeeper Harrison Devenish-Meares held his nerve to deny Kosta Grozos and Xavier Bertoncello in the shootout, before defender Ben Garuccio converted the winning spot kick.
The tie ended 2-2 on aggregate, but the Sky Blues claimed the tie 4-2 on penalties and will head across the Tasman to face Auckland FC in next Saturday's grand final at Go Media Stadium.
Led by interim coach Patrick Kisnorbo, Sydney will make their first grand final appearance since their 3-1 loss to Melbourne City in 2021.
Missing out on finals last year under Ufuk Talay, the Sky Blues will vie for a record sixth championship after just seven games under Kisnorbo.
Kisnorbo, who had guided City to victory in 2021, hailed the grit of his new side.
"To concede a goal with a minute-and-a-half to go, it can break teams. And it didn't," Kisnorbo said.
"The resilience and mental toughness the players showed in high-pressure moments, I was very pleased with.
"Nothing's done yet, but it's just showing belief and confidence within the group.
"Sometimes it's very hard to come in as a new coach, and you don't know where the group is at.
"I'm quite demanding, and they've been great.
"We still have another week to go. Preparation starts tomorrow."
It is a heartbreaking end to Newcastle's remarkable season under first-year coach Mark Milligan.
After winning their maiden premiership after 15 regular-season victories, the Jets missed out in their bid for a historic domestic treble after claiming the Australia Cup in October.
They haven't played for a championship since finishing runners-up to Melbourne Victory in 2018.
"This team did not overachieve," Milligan said.
"We did exactly what we were supposed to do, because I saw how much ability this group had.
"We had to give them a platform to allow them to express that.
"They earned everything that they got."
Peruvian international Quispe silenced the sold-out crowd of 25,082 fans after Jets goalkeeper James Delianov spilt the ball in denying Sydney teenager Akol Akon's goal attempt.
Newcastle were gifted a golden opportunity to level in the 83rd minute when Garuccio fouled Bertoncello just outside the box.
Adams took the kick, but sent the ball into the wall of Sky Blues defenders.
The relentless young winger eventually found redemption six minutes into added time after making the most of Daniel Wilmering's cutback to score.
Sydney were lucky to avoid giving away a penalty in an evenly-paced first half.
Garuccio had downed Adams by throwing himself at the goal-bound attacker in the 31st minute, but referee Shaun Evans let the moment go.
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