Tunisia beat France 1-0 on Wednesday night in their final game in Group D at the World Cup in Qatar.
Wahbi Khazri scored the only goal of the game in the 58th minute at the Education City Stadium.
Within seconds of his strike, Mat Leckie gave Australia the lead against Denmark at the Al Janoub Stadium.
It meant that for the last 35 minutes of the games, Tunisia had to hold on or even extend their lead and hope that Denmark would equalise but not go on to win.
However, Australia held firm to progress to the last 16 for the first time since 2006.
Elation
"We're pretty stoked," said Leckie, who was deemed man of the match.
"We want to dream big," added the 31-year-old, who plays for Melbourne City in Australia's A-League.
"We said we wanted to get out of the group and we've done that.
"The coach has obviously told us that we've got another game coming up so all we can do is get ourselves ready for that."
On Saturday night at the Ahmad Bin Ali Stadium, Australia will face Argentina after they claimed Group C on Tuesday night with a 2-0 victory over Poland.
Disappointment
When the draw for the World Cup was made, Denmark and France were lined up for the two places from Group D in the knockout stages: France for the array of talent at the disposal of coach Didier Deschamp, and Denmark on the basis of their run to the semi-finals at the European championships in 2021 and their form in the Nations League.
"We started the game against Australia really well," said Denmark boss Kasper Hjulmand.
"And we were getting into good positions and then the structure just went out and it became too emotional and there wasn't enough quality."
France, who are seeking to become only the third side in the 92-year history of the World Cup to win back-to-back titles, will take on Poland on Sunday at the Al Thumama Stadium.
