Australia advanced to the World Cup Round of 16 for the second time in history when Mathew Leckie's second-half winner knocked Denmark out in the group round.
The Socceroos started their Group D decider thinking a draw would suffice, but with Tunisia stunning France, who had already qualified, Graham Arnold's team, like the Danes, needed to win.
Denmark had many strong chances to take the lead in the first half, with Milos Degenek's spectacular block denying Jesper Lindstrom and Mat Ryan stopping a Mathias Jensen shot.
Instead, Australia, who had only appeared in the last 16 in 2006, broke the deadlock on the hour, springing Leckie on the counter-attack.
The Melbourne City attacker turned Denmark defender Joakim Maehle inside out before drilling a crisp left-foot shot low into the right corner.
The Danes, who had reached the knockout stages in four of their previous five World Cups, attempted a comeback, but the lack of cutting edge that had plagued their previous two group games continued to haunt them as Australia celebrated loudly after the final whistle.
Player ratings
Australia: Ryan (7), Degenek (6), Souttar (8), Rowles (6), Behich (7), Irvine (6), Mooy (6), Leckie (8), McGree (6), Goodwin (6), Duke (6).
Subs: Wright (5), Baccus (6), Hrustic (n/a), Maclaren (n/a).
Denmark: Schmeichel (5), Kristensen (5), Andersen (5), Christensen (5), Maehle (5), Hojbjerg (6), Jensen (6), Eriksen (6), Skov Olsen (6), Lindstrom (6), Braithwaite (4).
Subs: Bah (6), Damsgaard (5), Dolberg (5), Cornelius (5), Skov (5).
Player of the match: Mathew Leckie
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