Tuesday's other quarterfinal will be between German 10th seed Angelique Kerber and Italy's No. 21 Sara Errani.
Meanwhile, 15th seed Aravane Rezai recovered from a mid-match blip to see off Angelique Kerber 6-2 2-6 6-3.
Germany's Angelique Kerber will play Russia's Anastasia Pavlyuchenkova after she overcame Puerto Rica's Monica Puig 3-6 6-4 7-6.
At the WTA event in Paris, France's Marion Bartoli will face Germany's Angelique Kerber in the final on Sunday.
Among the seeded women to lose were No. 6 Angelique Kerber, No. 11 Nadia Petrova and No. 14 Maria Kirilenko.
Romania's Sorana Cirstea earned a clash with former world No. 1 Jelena Jankovic after eliminating German sixth seed Angelique Kerber 6-4 6-0.
Stosur's calf injury gifted Germany's fourth seed Angelique Kerber a place in the last four where she will now play Caroline Wozniacki.
Azarenka takes on German 18th seed Angelique Kerber in Friday's opening semifinal.
She will play Angelique Kerber of Germany, who battled past Wimbledon champion Petra Kvitova to reach her sixth semifinal of the season.
Germany's Angelique Kerber triumphed 6-2 7-5 over Russian qualifier Galina Voskoboeva who took a medical time out because of the extreme heat.
If she wins that game, Williams will play either German seventh seed Angelique Kerber or Hungary's Timea Babos for a place in the quarterfinals.
Sixth seed Angelique Kerber of Germany ended Venus Williams dreams of a third U.S. Open title with a 6-2 5-7 7-5 win over the American.
Fourth seed Angelique Kerber came through in three sets against Georgia's Anna Tatishvili, while her fellow German Sabine Lisicki beat Czech Lucie Safarova 6-2 6-4.
Fourth seed Agnieszka Radwanska eased past Irina-Camelia Begu, while there were also wins for German fifth seed Angelique Kerber and China's sixth seed Li Na .
Radwanska will face the tournament's surprise package Dominika Cibulkova in the final after the Czech world No. 15 beat German second seed Angelique Kerber 6-2 4-6 6-3.
Second seed Angelique Kerber of Germany had a much harder fight to dispatch Britain's Anne Keothavong, 4-6 6-3 6-3 and faces compatriot Mona Barthel in the quarterfinals.
Meanwhile at the WTA event in Stuttgart, defending champion Maria Sharapova booked at place in Sunday's final after beating Germany's Angelique Kerber in three sets 6-3 2-6 7-5.
Russian No. 2 Sharapova will play 20th-seeded compatriot Maria Kirilenko, while the remaining quarterfinal tie pits China's French Open champion Li Na against German No. 18 Angelique Kerber.
Azarenka beat Venus' conqueror Angelique Kerber, battling to a 6-4 7-5 win over the German seventh seed -- whose 48 match wins this year is the most on the WTA Tour.
STUTTGART, Germany (AP) Defending champion Maria Sharapova rallied in the third set to beat Angelique Kerber 6-3, 2-6, 7-5 Saturday and earn a spot in the final of the Porsche Grand Prix.
Seventh seed Vera Zvonareva defeated ninth seed Alona Bondarenko 6-2 6-1, 13th seed Melanie Oudin beat Christina Mchale 6-4 6-0, and eighth seed Daniela Hantuchova battled past Angelique Kerber 6-7 (6-8) 7-5 6-3.
It has proved an excellent work out for Sharapova as she builds up to the French Open defense, with hard fought wins over Lucie Safarova, Ana Ivanovic and Angelique Kerber on the way to the title match.
Two seeded players lost in the first round on Tuesday, as number 11 Olga Poutschkova was upset 6-0 6-0 by Angelique Kerber of Germany and number 10 Severine Bremond was defeated 4-6 6-3 6-4 by Alicia Molik.
Azarenka extended her unbeaten run to 22 matches, surpassing Serena Williams' start to 2003, as she beat German 18th seed Angelique Kerber 6-4 6-3 to claim the best beginning to a campaign since Martina Hingis went 37-0 in 1997.
The women's matchups Sunday to decide quarterfinal berths are: 15-time major champion Serena Williams against No. 15 Roberta Vinci, 2008 French Open titlist Ana Ivanovic against No. 4 Agnieszka Radwanska, 2009 champion Svetlana Kuznetsova against No. 8 Angelique Kerber, and 2012 runner-up Sara Errani against No. 20 Carla Suarez Navarro.
Former world No. 1's and Serbian Fed Cup teammates Ana Ivanovic and Jelena Jankovic will attempt to recapture their best results while German trio Sabine Lisicki, Julia Goerges and Angelique Kerber are likely to make a push in the absence of world No. 10 Andrea Petkovic who withdrew Wednesday, citing a stress fracture in her lower back.
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With top-ranked Azarenka and Serena Williams on the other half of the draw, Radwanska's main obstacles to reaching the final are 2011 French Open champion Li Na, who beat Olga Goortsova of Belarus 6-2, 7-5 to reach the third round, and potential semifinal rivals Sharapova or No. 5 Angelique Kerber, who advanced with a 6-3, 6-1 win over Lucie Hradecka.
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