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The top seed Barty defeated Madison Keys 6-1, 6-3 in the semifinals.
Nadal has reached his 14th quarterfinals of the Australian Open.
Barty's potential fourth round matchup against Osaka had been the talk of Melbourne Park.
The unseeded former world No. 1 won 6-3, 6-3 on Rod Laver Arena and faces 30th seed Anastasia Pavlyuchenkova of Russia in the last eight.
Ashleigh Barty overwhelmed British wild card Harriet Dart 6-1, 6-1.
Barty needed to win to be sure of progressing having won one and lost one of her opening matches, and she did so in style as she dominated to win in 88 minutes against a tired looking Kvitova, who exits the competition with three straight losses.
Ashleigh Barty joins Margaret Court and Evonne Goolagong-Cawley on the list of Australian women who have lifted the trophy.
Andreescu beat Serena Williams 6-3, 7-5 in Saturday's final to maintain a 13-match unbeaten run, where she also won the Canadian Open, to break into the top 10 for the first time in her career.
The Australian claimed a record-setting 4.42 million dollar paycheque - the largest sum ever awarded in men's and women's tennis.
Barty became the first Australian woman since Stosur in 2013 to reach the top 10 in the world rankings.
Results 1-10
