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The 55th-ranked Shvedova saved three match points at 5-4 on the Romanian’s serve in the 11th game of the second set and made a decisive break in the 12th game.
In the semifinals, Shvedova, who is looking for her second career title, will face Akgul Amanmuradova of Uzbekistan. Amanmuradova, the 2005 finalist, beat fifth-seeded Stefanie Voegele of Switzerland 6-1, 6-4.
Second-seeded Shahar Peer of Israel also advanced, beating Russian qualifier Alexandra Panova 6-4, 6-4. Peer is looking for back-to-back titles after winning the Guangzhou Open last weekend.
On Saturday, Peer will take on fourth-seeded Olga Govortsova of Belarus, who defeated Darya Kustova 6-3, 2-6, 6-2.