Top-ranked Serena Williams advanced to the Rogers Cup quarter-finals on Thursday, beating 16th-seeded Andrea Petkovic of Germany 6-3 6-2.

“I think I served better,” Williams said. “It was a big difference. I still think I have a tremendous amount of improvement to do off the ground and everywhere else.”

Williams won titles in Toronto in 2001, 2011 and 2013.

The 21-time Grand Slam singles champion will face Italy’s Roberta Vinci, a 6-4 6-3 winner over Russia’s Daria Gavrilova.

Second-seeded Simona Halep of Romania also advanced, outlasting 13th-seeded Angelique Kerber of Germany 6-3 5-7 6-4 in hot conditions.

“I did well in the last game,” Halep said. “I said, I have to win it because I cannot move anymore.”

Halep will face sixth-seeded Agnieszka Radwanska of Poland, a 6-2 4-6 6-4 winner over Alize Cornet of France.

Unseeded Belinda Bencic defeated Sabine Lisicki 6-1 1-6 7-6 (7-3) to keep her run going.

The 20th-ranked player from Switzerland opened the tournament with a victory over slumping Canadian Eugenie Bouchard and followed it with an upset win over fifth-ranked Caroline Wozniacki of Denmark.

Bencic will play the winner of Ivanovic and Hercog.

Also, 15th-seeded Sara Errani of Italy beat Belarus’ Victoria Azarenka 7-5 6-3 and Ukraine’s Lesia Tsurenko accounted for Germany’s Carina Witthoeft 6-3 6-4.