BEIJING -- Serena Williams had a far easier time than she did in her opening match, topping Tsvetana Pironkova in straight sets to advance to the third round of the China Open on Tuesday.
Williams, who rallied from a 5-0 deficit to beat Silvia Soler-Espinosa in the first round, cruised to a 6-2, 6-3 victory over Pironkova of Bulgaria.
"I wanted to start out strong, so that was the main difference, was just making sure I was able to win a game early on," she said.
Venus Williams, meanwhile, avenged a loss to France's Caroline Garcia at last week's Wuhan Open with a 6-4, 6-3 victory.
Five-time major winner Maria Sharapova, the fourth seed, also moved on with a 6-2, 6-2 second-round win over Elina Svitolina of Ukraine.
"She's sort of an up-and-comer but playing really well," said Sharapova, who saved seven of nine break points she faced. "She has had some big results this year against top players. Maybe the scoreline was a bit easier than the match showed."
Second-seeded Simona Halep won a tight match against 167th-ranked Lin Zhu of China, 7-5, 6-4, and No. 9 seed Ana Ivanovic of Serbia defeated Romina Oprandi of Italy 6-4, 6-2.
Agnieszka Radwanska's late-season slide continued with a 6-4, 6-4 loss to Roberta Vinci of Italy.
Since winning the Canadian Open in August, the fifth-seeded Radwanska hasn't advanced past the quarterfinals in her last five events. She could have wrapped up her spot in the season-ending WTA Finals this week, but fell in the second round in both Wuhan and now Beijing.
No. 8 seed Eugenie Bouchard, a finalist in Wuhan, fell to Sabine Lisicki of Germany 6-2, 6-4.