Kerber saved two set points but then produced a double-fault to give it away.
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.
But her strong finish in the last two games allowed Sharapova to improve to 4-1 against the sixth-ranked Kerber.
At the WTA event in Paris, France's Marion Bartoli will face Germany's Angelique Kerber in the final on Sunday.
Five straight games saw Kerber romp to victory in front of the stunned home crowd at the Farum Arena.
Kerber battled past the second seed 7-6 5-7 6-3 to land her first career title after a superb week.
Among the seeded women to lose were No. 6 Angelique Kerber, No. 11 Nadia Petrova and No. 14 Maria Kirilenko.
Kerber took the opener and led 3-0 in the second set until Bartoli battled back in typical style to level.
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.
The 24-year-old Kerber again opened up a 3-0 advantage in the decider and this time held on to seal a memorable victory.
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.
Kerber, the second seed, had also lost her two previous meetings to Wozniacki, but staged a recovery in each set to claim victory.
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 .
After being taken the distance by Lucie Safarova and Ana Ivanovic in the previous two rounds, Sharapova dominated the first set of the semifinal breaking Kerber twice.
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.
The second seed beat Klara Zakopalova from the Czech Republic 7-6 6-0 to set up a meeting with Kerber who beat Yanina Wickmayer from Belgium 6-7 6-3 6-4.
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.
Serena and Venus also won their opening doubles match, beating Romania's Sorana Cirstea and Simona Halep 6-3 6-2 to set up a clash with Kerber and Sabine Lisicki.
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