Li defeated Mandy Minella 6-4, 6-0 without facing a break point and winning more than 60 percent of the points in the match. In the second set Li lost only 11 points -- three on serve -- in finishing off the win in 64 minutes.
Sixth-seeded Peng Shuai needed only 52 minutes to rout Ayumi Morita 6-1, 6-1. The game she lost in the first set was a service break, but she won all 12 of her points serving in the second set to advance.
Also in the second round, Klara Zakopalova, the fifth seed, defeated Elina Svitolina 6-4, 6-3 and eighth-seeded Bojana Jovanovski stopped Duan Ying-Ying 6-3, 6-1, but Annika Beck and Monica Niculescu each gained third-round berths with upset wins.
Beck blitzed fourth-seeded Hsieh Su-Wei 6-3, 6-0 in less than an hour by piling up three breaks in each, set and Niculescu took out No. 7 Laura Robson 6-2, 6-3 without losing her serve.
Zhou Yi-Miao, in the draw in place of third-seeded Jelena Jankovic who withdrew Tuesday, beat Jessica Pegula 6-4, 6-2.
Celebrity Families of 2014 [PHOTOS]