Seventh-seeded Samantha Stosur advanced to the second round of the Kremlin Cup by beating Kaia Kanepi 6-3, 6-1 on Wednesday.
Stosur, coming off her second title this season and fifth of her career, converted four of 11 break opportunities.
"I played really well today and Kaia was a really dangerous opponent," Stosur said. "I really tried to start the match well, on top."
A runner-up her last season, Stosur will next play Alize Cornet.
Two-time Grand Slam champion Svetlana Kuznetsova advanced to the quarterfinals by beating Sofia Arvidsson 6-2, 7-5.
Kuznetsova, currently ranked 23rd, overcame an early break in the second set and earned the victory on her third match point.
"I felt myself much better today and was more relaxed on the court," Kuznetsova said. "Yet, I was hurrying a bit and wanted to play more aggressive, thus making more mistakes. But I can say that now, by the end of the season, I play much better."
In the men's second round, defending champion Andreas Seppi broke Paolo Lorenzi twice in the second set to win 6-3, 6-2.
"I think I played a solid match today performing very aggressive tennis," Seppi said. "It was a good start of the tournament for me."
In the quarterfinals, the second-seeded Seppi will face Edouard Roger-Vasselin, who ousted Sergiy Stakhovsky 7-5, 7-5.
Earlier, Alisa Kleybanova advanced to her first quarterfinal since being treated for cancer, beating the sixth-seeded Carla Suarez Navarro 7-6 (2), 6-4.
The 24-year-old Russian was ranked as high as 20th, but after missing much of the last two seasons because of her illness is now 254th. She resumed her career in May and won a challenger event before returning to the WTA Tour in Toronto in August.
"I always liked to play with Carla and I knew it would be a tough match today," Kleybanova said. "But I think that today I played more accurate on key moments and that's why I won."
Kleybanova was diagnosed with blood cancer and underwent chemotherapy until December 2011.
Anastasia Pavlyuchenkova, who is looking for her third title of the season, beat Russian compatriot Maria Pavlyuchenkova 6-3, 6-3 to reach her seventh quarterfinal.