Toronto, Aug 9 (IANS): World No.1 and top seed Serena Williams breezed into the Rogers Cup quarter-finals after a stunning 6-0, 6-3 victory against Belgium's 13th-seeded Kirsten Flipkens here, while China's Li Na had to fight hard to overcome Ana Ivanovic of Serbia to book her berth in the last 16.

Williams, a two-time Rogers Cup champion, who received a bye in the first round and nabbed a 6-3, 6-2 win against Italy's Francesca Schiavone Wednesday night, met Flipkens for the first time on the court Thursday, reports Xinhua.

She dominated the entire match against Flipkens, who had ousted her sister Venus in the first round earlier this week.

"I definitely thought about Venus, and I thought about what a great comeback Kirsten had, so I thought that I'm not going to get overconfident and she's obviously a really good player," Serena told reporters.

"So I was just trying to stay focused as well as intense, I really wanted to stay intense at that moment."

Serena is up against Slovakia's Magdalena Rybarikova in the quarters, after Wimbledon champion Marion Bartoli had to pull out of their third-round match early Thursday due to injury.

The French player ended the second set of her third-round match against Rybarikova, who was leading 7-6 (5), 1-0.

Prior to Williams' match, China's only Grand Slam champion Li Na -- seeded 4th in the event -- was on the brink of defeat when she launched an aggressive attack against Serbia's Ana Ivanovic to fight her way into the quarterfinals 6-3, 1-6, 6-7(5).

She will face Slovakia's Dominika Cibulkova next.

Earlier in the day, Polish player Agnieszka Radwanska, No.3 seed, defeated Australian Open semifinalist Sloane Stephens with a 6-1, 7-6 (2) victory.