For the first time in 16 years, Australia made it to the knockout stage of the World Cup.
Australia scored the winner on the hour mark after the Danes dominated possession.
Mathew Leckie scored on a counter attack after the Danes lost the ball in the Australian box.
Australia finished second in Group D with six points, only behind world champion France.
The Danes exited the group with just one point from three games.
Poland, Argentina, Saudi Arabia and Mexico have a chance of topping the table if they beat Australia on Saturday.
The Danes were tipped by fans and pundits as dark horses after their run to the semi-finals of Euro 2020 and a strong Nations League campaign.
They only scored once in three games in Group D, and failed to impress.
Three changes were made from the defeat to France, all in attacking positions.
The changes didn't make a difference.
In the first half, Jensen forced Mat Ryan into an acrobatic save after being played through by a Braithwaite flick.
It was clear that Joakim Maehle, the left back who tested Australia with his probing runs, was not supported by those further forward.
The Danes wanted a penalty in the second half when Dolberg was hauled down in the area, but he was not in a good position.
The Danes have failed to win any of their past six games in the competition and have four draws.
Australia, the lowest ranked side in Group D, ran the game at their pace and the largely boring encounter suited their needs perfectly, with a draw potentially enough to see them through having started the day second in the group.
As the news of Tunisia taking a shock lead against France trickled in, Leckie sprang into action.
The Australians caught out on the break after Dolberg lost the ball. Leckie ran confidently at the Danes, and hit left footed through Maehle's legs past the far post.
They reached the last 16 of the World Cup for the first time since 2006 when a star- studded side featuring Harry Kewell, Tim Cahill and Mark Schwarzer were only stopped by Italy.
This team is marshalled by captain and former Seagulls goalkeeper Ryan, and they have recovered from their opening loss to France, where they were naively open and picked apart, to grind out the results required.
Ryan was the one who led Australia through the last six minutes of added time.
A historic victory was secured when a Cornelius headed the ball onto the roof of the net in the final seconds of the game.
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