All three teams finished on six points but Australia qualified second in the group with a goal difference of 7-3 ahead of the Korean's goal difference of 5-3.
Australia will now meet Asia's top ranked side North Korea in the semi-finals on Thursday. The other semi final will feature Japan and China.
"Whilst I am disappointed with the result and that we some lapses of concentration in defence, I am delighted with the character the team showed in claiming a semi final spot," said coach Tom Sermanni.
"Our team showed tremendous sprit and determination to come from behind to pull the goal back that we ultimately needed to reach the semis.
"Although the Japanese team had a largely unchanged line-up from the match two days ago, we had virtually the same team yet we finished the stronger which is a testament to this group of players."