Li, the No. 4 seed, easily handled Bojana Jovanovski 6-2, 6-1 in 53 minutes. Jovanovski had won 14 of her last 15 matches, picking up a pair of WTA titles in the process.
But Li dropped only six points on serve and was 6-for-6 in break opportunities to gain a spot in the third round. She ended up winning 69 percent of the points in the match.
World No. 1 Serena Williams also advanced in straight sets but in a much more difficult match, beating Francesca Schiavone 6-4, 7-5 in 1 hour, 47 minutes. Williams notched the only break of the first set but needed three breaks in the second as Schiavone was 2-of-7 in break chances in the set.
No. 6-seeded Carolina Wozniacki came out a 6-3, 6-1 winner over Monica Niculescu as she had six breaks in Niculescu's eight games serving and Angelique Kerber, seeded seventh, raced past Laura Robson 6-1, 6-2.
Ninth-seeded Petra Kvitova got by Varvara Lepchenko 2-6, 6-2, 6-0 while 10th-seeded Roberta Vinci outlasted Zhang Shuai 3-6, 6-3, 6-1. Sloane Stephens, the 11th seed, took a 6-1, 1-6, 6-4 decision from Eugenie Bouchard; No. 12 Carla Suarez Navarro beat Lauren Davis 6-4, 6-2; and 13th-seeded Sabine Lisicki ousted Venus Williams 6-1, 6-2.
Maria Kirilenko defeated Urszula Radwanska 6-4, 6-4 in the only match Tuesday between unseeded players. Kirilenko earned a third-round match against Serena Williams with the win.
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