Iran Press/ West Asia: Australia had taken the lead just before halftime when they cleverly switched flanks with neat passes in the box before Nathaniel Atkinson's cross found Craig Goodwin, who had time to set himself up for a volley into the bottom corner.
Martin Boyle could have made it 2-0 when he received a cross into the box but goalkeeper Jo Hyeon-Woo made two saves to deny him while Mitchell Duke's volley from the rebound went over the bar to give South Korea a reprieve.
Klinsmann made a tactical change in the second half, pushing Son further forward and the strategy worked when the Tottenham Hotspur forward was fouled in the box by Lewis Miller in the fourth minute of stoppage time.
Hwang Hee-chan stepped up and the Wolverhampton Wanderers forward took his time to calm his nerves before he fired his effort into the top corner to force extra time -- their fourth goal after the 90th minute at the tournament.
"I'm usually the first kicker but I was fatigued and Hwang was confident to step up and take the penalty, so I said ok. He's a very important player and he a good chance to prove he's important," Son said.
With South Korea going to extra time for a second straight game after they beat Saudi Arabia on penalties, Hwang won a free kick on the edge of the box from a foul conceded by Miller once again.
Son stepped up and saw his effort sail past the wall, beating Mathew Ryan in goal to find the net and spark wild celebrations with Klinsmann also letting out a roar with his arms raised.
Australia's attempts to fight back suffered a blow when Aiden O'Neill was sent off after a VAR review for a foul on Hwang, reducing Graham Arnold's side to 10 men for the second half of extra time where they could not find an equaliser.
Australia had beaten South Korea by the same scoreline in extra time in the 2015 final to lift their first Asian Cup, but this time it was the east Asian team who prevailed after netting yet another goal in stoppage time to force extra time.
South Korea play Jordan on Tuesday in the first semi-final after the Middle Eastern side beat Tajikistan 1-0 earlier on Friday. South Korea had grabbed a late equaliser in a 2-2 draw against Jordan in the group stage.
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South Korea beats Saudi Arabia to reach Asian Cup last eight
