Australia made Women's World Cup history after stunning Brazil 1-0 in their last-16 clash on Sunday.
The Matildas had never won a knockout fixture at a World Cup, despite progressing beyond the group stages in 2007 and 2011.
The Socceroos - their male counterparts - have only ever contested one sudden-death World Cup match in 2006 and lost.
Alen Stajcic's women broke new ground for Australia in remarkable fashion thanks to substitute Kyah Simon, who netted the match-winning goal with 10 minutes remaining at Moncton Stadium in New Brunswick.
Simon - a second-half replacement for Michelle Heyman - scored a close-range rebound as Australia shocked their highly-fancied opponents for a spot in the quarter-finals.
Australia will play the winner of Japan versus Netherlands on June 27.
Host nation Canada and France also progressed to the last eight on Sunday.
Josee Belanger was the hero for Canada, with her 52nd-minute goal sending the Vancouver crowd into a frenzy and seeing the hosts past Switzerland 1-0.
Next up for Canada is either Norway or England.
As for France, they will face two-time champions Germany in the last-eight after defeating South Korea 3-0.
Two quick-fire goals from Marie-Laure Delie and Elodie Thomis set the tone in Montreal, before the former completed the scoring early in the second half.
