Fridolina Rolfö put a zero to Sweden in the 20th minute after a dubious opening of the match from Sweden.
Before the half, Australia equalized through a header by Sam Kerr in the 36th minute.
Australia then wanted a penalty when Sam Kerr collapsed in the penalty area after a tackle from Hanna Glas.
But the referee did not agree and the game went on.
Rolfö slams again
Just minutes into the second half, Sam Kerr could then easily nod in two one to Australia.
But Sweden gave a quick response to the lead goal, Lina Hurtig equalized in the match minute 52 to two two.
Sweden then had a good period in the match with a game that was more similar to what they had against the USA.
Fridolina Rolfö then slammed in with a left shot from the penalty area line and with her second goal in the match, she gave Sweden in a three two-lead.
Ready for the quarterfinals
Shortly afterwards, Australia got a penalty and Sam Kerr was given a chance to score a hat-trick in the match.
But Hedvig Lindahl stood firm in the goal and her rescue kept Sweden in the lead.
A lead that substitute Stina Blackstenius could then extend to 4-2 after a nice post from Kosovar Asllani.
The result stood out since the match and Sweden is thus ready for the Olympic quarter-finals.
- In a way, this result impresses me more than the match against the USA. When not everything works and when their own and others' expectations are not met, they turn a disadvantage, says SVT sports expert Markus Johannesson.