The Socceroos will face Lionel Messi's Argentina side in the World Cup round of 16 in Qatar on Sunday morning, Newcastle time.
A stunning solo goal from Mathew Leckie sunk Denmark 1-0 in the early hours of Thursday AEDT and sent Australia into the knockout stage for just the second time.
A few hours later, Argentina put two goals past Poland to go from a first round loss to the top of Group C.
It means Australia, ranked 38th in the world, will face third ranked Argentina in an elimination match at 6am AEDT on Sunday.
Leckie's superb left-footed strike ensures the Socceroos follow the feats of the so-called golden generation in 2006 in reaching the round of 16.
The stalwart, played into space by Riley McGree, broke an hour-long deadlock with a slicing run at his marker Joakim Maehle after gathering some 30 metres from goal.
First to his right, then onto his left, Leckie twisted and turned his opponent and fired a low left-footer to instantly enter Australian football folklore.
"As the ball was rolling in, I saw it going in, I was so excited and so happy," Leckie said pitchside.
"By the celebration you see how much emotion there was.
"I'm just so proud. We've worked so hard.
"This is my third World Cup now and I've had my chances in previous World Cups to score, wasn't meant to be.
"My first World Cup (goal) is probably one of the most important goals for me and for the team."
Leckie's timing was perfect in more ways than one.
In the other simultaneous game in Australia's group on Wednesday (Thursday AEDT), outsiders Tunisia had scored just three minutes earlier against holders France, who rested almost their entire first-choice side.
The Tunisian goal momentarily lifted them to second in the group behind the French only for Leckie to restore the Socceroos into that prized slot.
Leckie and his captain Mat Ryan, barring injury, will break the Australian record for most cup games in the knockout encounter this weekend.
Against the Danes, the duo both made their ninth cup appearance, equalling Tim Cahill and Marco Bresciano's record.
Goalkeeper Ryan was called into action early as the Socceroos lacked early spark and were forced to repel a series of attacks from the Danes, ranked 10th in the world, 28 slots higher than Australia.
Ryan made a reflex save in the 11th minute from a thundering Mathias Jensen shot, the Australian parrying away with both hands above his head.
The Danes controlled two-thirds of possession, having almost double the passes of Australia in the opening half yet the Socceroos crafted some half-chances mainly courtesy of midfielder Riley McGree.
The attacking midfielder had the first shot of the match - a long-range left footer in the third minute which was blocked in the box - and another some 20 minutes later after Leckie and Mitch Duke headers played him into space.
After a scoreless half, Socceroos coach Graham Arnold replaced Craig Goodwin, who lacked his customary fizz on the flank, with Keanu Baccus.
And Arnold must have revved up his players, who produced a much improved second half to create another landmark.
"We always knew we could do it. We believed as a group," Leckie said.
"We had our doubters. With our spirit, our belief, our work ethic and how close we are as a group, it shows on the pitch.
"That last 15, 20 minutes, we battled until the end. It didn't matter what they threw at us, we weren't conceding."
Australian Associated Press
