As expected, it was Argentina who took the lead from the start.
And just over half an hour in, the goal arrived - signed by Lionel Messi.
Messi sneaked his in towards the center from the right wing position and got the ball at his feet just inside the penalty area line after nimble passing.
From there he was cool himself and placed the ball wide left at the far post.
The goal was Messi's ninth career World Cup goal and with it he moved away from the joint second place he shared with Diego Armando Maradona with most World Cup goals for Argentina (Gabriel Batistuta leads with ten World Cup goals).
The goal was also Messi's first in a World Cup play-off match.
In the second half, Australian goalkeeper Mat Ryan was up for an invitation when, under pressure, he tried to run away with the ball.
Instead, Julian Alvarez appeared and rolled the ball into the gaping empty goal for 2-0.
Australia fought back
But Australia did not give up.
In the 77th minute, the reduction came after Craig Goodwin unleashed a shot from outside the penalty area that took a solid touch on Enzo Fernandez and into the goal.
Just a couple of minutes later, Australia were about to equalize after Aziz Behich broke from his left-back position in midfield and slipped past four or five Argentine players and into the penalty area.
But just as he was about to shoot, Lisandro Martinez came up with a saving shot block.
But a better chance to equalize never came against an Argentinian defense that tightened up after the shocking minutes.
The promotion means that Argentina will face the Netherlands in the quarter-finals on Friday, December 9, a match that will be broadcast on SVT1 at 20:00.
Highlights from Argentina-Australia
Messi scores - goes past Maradona
24 sec
Alvarez takes advantage of the goalkeeper's giant blunder
21 sec
Australia reduce after the odd goal
16 sec
Discussed the situation: "Could very well have been a penalty"
32 sec