Son Heung-min's last-gasp goal had sent a captivating contest into an additional 30 minutes as Massimo Luongo's first-half strike was cancelled out in dramatic fashion on Saturday.
But, having come off the bench with 19 minutes of normal time remaining, Troisi was the Socceroos' hero as the home side capitalised on some woeful defending to win it in the first extra period.
The result offered a long-awaited tonic to the heartache of four years ago when Australia lost the final 1-0 to Japan, while it also served up revenge for the group-stage loss to the Koreans just a fortnight ago.
And it also vindicated coach Ange Postecoglou's regeneration of the squad since he took the role 14 months ago.
A sell-out crowd of almost 77,000 made for a cracking atmosphere in Stadium Australia, offering all the ingredients for what proved to be a special night.
South Korea had not conceded a goal in the tournament until Luongo's opener on the stroke of half-time, but it had been coming.
Mile Jedinak threatened first with a dipping long-range free-kick, while Kwak Tae-hwi headed just wide from Ki Sung-yueng's set-piece at the other end.
Finally Luongo intervened to break the deadlock, building on his ever-growing reputation after a stellar tournament.
The Swindon Town midfielder received a pass 30 yards from goal and showed excellent poise to bring the ball under control before taking a stride forwards and rifling home.
Chasing the game, it was no surprise Uli Stielike's side lifted the tempo in the second half.
Set-pieces were causing Australia trouble and Kwak got on the end of another free-kick, only to head straight at Mat Ryan.
The Socceroos were not about to park the bus and Mathew Leckie forced a smart save on the hour mark before Trent Sainsbury headed just wide from the resulting corner.
As fatigue started to set in Postecoglou called on the fresh legs of Tomi Juric and Troisi for Tim Cahill and the injured Robbie Kruse.
But the pressure told in stoppage time, when Australia failed to deal with a bouncing ball and Ki slid in Son, who produced a classy finish.
Australia had to pick themselves up off the canvas and did so late in the first half of extra time, with a little help from the opposition defence.
Two South Korea defenders failed to prevent Juric, who twice fell over, from cutting inside along the byline before his cross was parried into the path of Troisi to net the winner and send the home crowd wild.
