Australia had been the form team with two big wins so far, but Ange Postecoglou's rejigged side were dealt a setback after the Korean striker slid in to score on 32 minutes.
The Socceroos, who finish second in Group A, will now play China in the quarter-finals in hot and humid Brisbane and face a likely semi-final against holders Japan.
Australia threw everything at South Korea as they sought a vital equaliser, and Kim Jin-Hyeon saved brilliantly from Robbie Kruse when the substitute looked certain to score.
"I definitely feel that we could have got a draw out of the game," said talismanic forward Tim Cahill, who came on in the second half but this time was unable to rescue Australia.
"Korea took their chance, full credit to them. But I definitely feel like we could have finished top of the group."
- Chorus of boos -
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With clouds of moths swarming around Brisbane Stadium, Kwak Tae-Hwi nodded wide and Tomi Juric's fierce shot was saved at the near post as the teams exchanged early chances.
Captain Ki Sung-Yueng threaded the ball to Lee Keun-Ho, whose cross-shot to the far post was met by the sliding Lee Jeong-Hyeop with Aussie goalkeeper Mat Ryan given no chance.
The goal rocked Australia but after striking eight times in their first two games, they would have been confident of hitting back in front of a sell-out crowd in Brisbane.
