Son Heung-min scored a brilliant extra-time free-kick to send South Korea to the Asian Cup semi-finals, having been seconds away from losing to Australia.
Australia had looked set for victory thanks to Craig Goodwin’s volley from Nathaniel Atkinson’s cross.
But Son was fouled by Lewis Miller and Hwang Hee-chan’s 96th-minute penalty sent the game to extra time.
Australia ended with 10 men after Aiden O’Neill was sent off by the video assistant referee for a dangerous foul.
South Korea, who last won the Asian Cup in 1960, were on the brink of elimination for the second round in a row.
In the last 16, Cho Gue-sung’s 99th-minute equaliser denied Saudi Arabia with the Koreans winning on penalties.
This win could help relieve some pressure on Jurgen Klinsmann, who was appointed a year ago and is unpopular with the Korean fans.
Jordan will be South Korea’s opponents in Tuesday’s semi-final after a 1-0 win over Asian Cup debutants Tajikistan.
Iran face Japan and hosts Qatar play Uzbekistan in Saturday’s other two quarter-finals.