Sam Stosur, Francesca Schiavone, Victoria Azarenka and Elena Dementieva also won but Dinara Safina was beaten.
Australia's Sam Stosur is the fifth seed, with four-time Wimbledon champion Serena Williams seeded sixth.
Sam Stosur rounded off Tuesday's play with a 6-4 6-4 win over French Open champion Francesca Schiavone.
After Sharapova and Kvitova, the highest-ranked player remaining in the last eight is U.S. Open champion Sam Stosur.
Australian second seed Sam Stosur joined Serena in the third round after defeating American wildcard Jamie Hampton 6-0 7-5.
The women's quarterfinals were blighted by injury after defending champion Victoria Azarenka and seventh seed Sam Stosur both pulled out with injury.
The women's 2011 winner Sam Stosur was drawn against Croatia's Petra Martic, with top seed Victoria Azarenka playing world No. 74 Alexandra Panova.
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Her last two U.S. Open exits against Kim Clijisters and Sam Stosur were anything but pretty, punctuated by diatribes worthy of John McEnroe.
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Elsewhere, home favourite Sam Stosur crashed out after throwing away a 5-2 lead in the final set before losing 6-4 1-6 7-5 to China's Zheng Jie .
The shocks did not stop there as home hope and seventh seed Sam Stosur was beaten in the night match by Swede Sofia Arvidsson, going down 7-6 7-5.
Williams will now face Maria Sharapova in the semifinal after the Russian defeated Australia's Sam Stosur 6-2 6-4, while Victoria Azaraenka also progressed to the last four after defeating Sara Errani.
Hampton, ranked 54th, upset Czech seventh seed Petra Kvitova 6-1 7-6 (9-7) to earn a clash with Serbia's former world No. 1 Jelena Jankovic -- who eliminated Australia's 2010 runner-up Sam Stosur despite losing the first set.
Serena powered to a 6-4 6-2 win over Australian Sam Stosur to book a meeting with Belarusian Victoria Azarenka, who recovered from a set down to beat Russia's Vera Zvonareva 4-6 6-4 6-0 in two hours and 28 minutes.
Monday proved an excellent day for the seeded women as Elena Dementieva (5), Sam Stosur (7), Agnieszka Radwanska (8), Li Na (11), Lucie Safarova (24), Alisa Kleybanova (28) and Kateryna Bondarenko (32) all went through without dropping a set.
Home favourite Sam Stosur , the fifth seed, made short work of Vera Dushevina, beating the Russian 6-3 6-2 to secure a third-round match against the Czech Republic's 25th seed Petra Kvitova , who beat Russia's Anna Chakvetadze 6-3 6-4.
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