Ben Garuccio sealed the shootout after Sydney goalkeeper Harrison Devenish-Meares saved Xavier Bertoncello's effort, leaving most of a sold-out crowd at McDonald Jones Stadium devastated.
Patrick Kisnorbo's Sydney will bid for a record-extending sixth league title at Auckland FC, having been held 1-1 at home by the Jets in the first leg.
"I kind of had my spot, I was confident with it," said Garuccio of his winner.
"It worked out. The boys were so good.
"I think (Devenish-Meares) has been the best keeper in the league by a country mile."
Piero Quispe put Sydney 1-0 up in the 64th minute and the visitors defended grimly to be within seconds of victory but Newcastle winger Eli Adams conjured a last-gasp equaliser in the sixth minute of injury time.
Newcastle won the Australian Cup in the off-season and the Premier's Plate for finishing top of the table at the end of the regular season.
But their bid to become the first team to complete Australian football's "triple crown" fell one trophy short.
"We've had so many amazing memories this year. Football can be cruel at times but I'm just so incredibly proud of what this team has done together -- along with the fans," said Newcastle playmaker Max Burgess.
In a see-sawing, high-tempo contest, neither side could convert until Sydney striker Apostolos Stamatelopoulos carved open Newcastle's defence with a trademark gallop down the right flank and crossed to 16-year-old wunderkind Akol Akon.
Akon's shot was parried by Delianov but pint-sized Peruvian Quispe was on the spot, swooping on the rebound to tuck the ball home.
Newcastle peppered the Sydney goal in search of an equaliser but were repeatedly thwarted.
With seconds ticking down to full-time, Daniel Wilmering whipped a low-driven cross into the area, finding Adams who volleyed it goalwards, sending the match into extra time and Newcastle fans into delirium.
Sydney FC had a glorious chance to settle the matter late in extra time when Alexandar Popovic rose highest for a corner, but he hammered his close-range header straight at Delianov.
Delianov denied the visitors again when he blocked Joe Lolley's opening effort in the shootout with an acrobatic dive.
But Devenish-Meares answered from the next kick with his own brilliant save to foil Newcastle captain Kosta Grozos and then Bertoncello, clearing the way for Garuccio's winner and another Sydney tilt at the title in Auckland in a week's time.