Williams, seeded third and the winner of the last two Grand Slam events, pasted Edina Gallovits-Hall 6-0, 6-0 in 54 minutes. Williams rolled her right ankle in the fifth game of the match but after a short medical timeout returned to the court and took the next eight games.
Williams lost only 18 points in the match, with just seven of those coming in her six serving games.
Defending champion and world No. 1 Victoria Azarenka won 57 percent of the points when receiving serve in defeating Monica Niculescu. She won 70 percent of the points overall in the first set in establishing control of the match.
Other upsets Tuesday saw Lesia Tsurenko slip past 24th-seeded Anastasia Pavlyuchenkova 7-5, 3-6, 7-5; Annika Beck top No. 28 Yaroslava Shvedova 6-2, 6-7 (7-9), 6-3; and Jamie Hampton oust 31st-seeded Urszula Radwanska 6-2, 6-4.
Eighth-seeded Petra Kvitova needed three sets to get by Francesca Schiavone 6-4, 2-6, 6-2 and No. 10-seeded Caroline Wozniacki came back for a 2-6, 6-3, 6-3 win over Sabine Lisicki. Among other high seeds, No. 14-seeded Maria Kirilenko beat Vania King 6-4, 6-2 and 16th-seeded Roberta Vinci stopped Silvia Soler-Espinosa 6-3, 7-5.
Other seeded players moving into the second round Tuesday were No. 17 Lucie Safarova, 20th-seeded Yanina Wickmayer, No. 21 Varvara Lepchenko, 26th-seeded Hsieh Su-Wei and 29th-seeded Sloane Stephens.
Unseeded winners Tuesday included: Svetlana Kuznetsova, Laura Robson, Jana Cepelova, Ayumi Morita, Yulia Tsurenko, Peng Shuai, Elena Vesnina, Bojana Jovanovski, Daria Gavrilova, Garbine Muguruza, Shahar Peer, Akgul Amanmuradova, Eleni Daniilidou, Donna Vekic, Kristina Mladenovic and Luksika Kumkhum.
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