Mathew Leckie claimed a fine second-half winner as Australia masterminded a World Cup shock by progressing to the knockout stages with a 1-0 victory which eliminated Denmark.
The Socceroos and the Danes were both in danger of crashing out of the tournament due to Tunisia taking the lead against reigning champions France in the other Group D fixture.
But Leckie had other ideas and delivered the knockout blow for the Danes with a superb solo effort in the 60th minute to send Australia into the last 16 for the first time since 2006.