Massimo Luongo put Australia ahead in the first half of regular time with a sizzling finish, receiving a good pass from Trent Sainsbury.
But South Korea got a deserved equalizer when star midfielder Son Heung-min scored in the dying seconds of the second-half to send the match to extra time.
James Troisi wrote his name in Australian football history with the winner late in extra-time.
On Friday, the UAE had defeated Iraq 3-2 and finished in third place.
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