Williams, the world No. 1, dispatched Caroline Garcia 6-1, 6-2 in 62 minutes and has lost a total of four games in the first two rounds of the tournament. Williams dropped just seven points serving and didn't face a break point.
Fourth-seeded Agnieszka Radwanska also gained a third-round berth in just 67 minutes as she beat Mallory Burdette 6-3, 6-2. She had a mere five unforced errors and won 60 percent of the points in the match, including 55 percent off Burdette's serve.
No. 3-ranked Victoria Azarenka picked up a delayed first-round win with a 6-1, 6-4 romp over Elena Vesnina. Azarenka had four breaks -- two in each set -- and lost her own serve just once. She also had just 13 unforced errors.
Petra Cetkovska best 19th-seeded Russian Anastasia Pavlyuchenkova 7-5, 2-6, 6-4, Kaia Kanepi ousted 23rd-seeded Klara Zakopalova 7-6 (7-3), 6-2 and Jamie Hampton posted a first-round upset of 25th-seeded Lucia Safarova 7-6 (7-5), 3-6, 9-7.
Dinah Pfizenmaier won a second-round match while unseeded winners Wednesday included Anna Karolina, Annika Beck, Peng Shuai, Stefanie Voegele, Ashleigh Barty, Petra Cetkovska, Svetlana Rybarikova, Monica Puig, Virginie Razzano, Carla Suarez Navarro.