Updated

World No. 1 Victoria Azarenka and last year's Wimbledon champion Petra Kvitova were easy second-round winners Wednesday at the 2012 U.S. Open.

The Belarusian star Azarenka whipped Belgian qualifier Kirsten Flipkens 6-2, 6-2 in 65 minutes at Ashe Stadium. Flipkens is a former U.S. Open girls and junior world champion.

Azarenka, a former U.S. Open mixed doubles champ, has been No. 1 for most of the year after capturing her first major singles title at the Australian Open back in January.

The 23-year-old Azarenka has never advanced beyond the fourth round in Flushing.

"I don't feel like I have to prove something," Azarenka said.

Next up for the Olympic bronze medalist Azarenka will be China's Zheng Jie.

The fifth-seeded Kvitova handled France's Alize Cornet 6-4, 6-3 at Armstrong Stadium. The left-handed Czech slugger, who captured both Wimbledon and the prestigious season-ending WTA Championships last year, is the only woman to reach the quarterfinals at all three Grand Slam events so far this year.

Kvitova's third-round opponent will be France's Pauline Parmentier.

Ninth-seeded Chinese Li Na continued her recent run of fine play with a 6-4, 6-4 victory over Aussie Casey Dellacqua. The 2011 French Open champion is fresh off her big hardcourt title in Cincinnati and was a runner-up to Kvitova in Montreal earlier this month.

Also, 15th-seeded Czech Lucie Safarova held off Canadian Aleksandra Wozniak 6-3, 4-6, 6-2, Frenchwoman Kristina Mladenovic dismissed 17th-seeded Russian Anastasia Pavlyuchenkova 6-1, 6-2, and 19th-seeded former top-10 Russian Nadia Petrova pasted Romanian Simona Halep 6-1, 6-1 on Day 3 at the USTA Billie Jean King National Tennis Center.

In other action involving seeds, Parmentier knocked out No. 25 Belgian Yanina Wickmayer 7-6 (7-5), 6-3, a No. 28 Zheng drubbed Slovak Magdalena Rybarikova 6-3, 6-1, and No. 31 American Varvara Lepchenko whipped Aussie Anastasia Rodionova 6-2, 6-2.

Another American winner was Stanford All-American Mallory Burdette, who surprised capable Czech Lucie Hradecka 6-2, 6-4.

Burdette is a 21-year-old from Georgia who was this year's NCAA runner-up to Nicole Gibbs, who lost in the first round this week.

"To end up here at the U.S. Open was a huge surprise," Burdette said. "I never expected that at the beginning of the summer."

Also advancing to the third round was Luxembourg's Mandy Minella.