Sharapova, the 2008 champion and two-time (2007, 20012) runner-up, lost only 23 points in a 6-0, 6-0 shutout of Olga Puchkova in 55 minutes. Sharapova allowed Puchkova just two break opportunities and had only 11 unforced errors.
Williams, the No. 25 seed, was on the court an hour in a 6-1, 6-0 win over Galina Voskoboeva. She saved all four of the break points she faced while posting 21 winners against 10 unforced errors.
Only one seeded player fell on the women's side Monday. No. 32 Mona Barthel, coming off a runner-up finish Saturday in Hobart, dropped a 5-7, 6-2, 4-6 decision to Ksenia Pervak in a tight 2-hour, 22-minute match.
Fourth-seeded Agnieszka Radwanska, with two titles on her 2013 resume already, took out Bojana Bobusic 7-5, 6-0, dropping just nine points in the second set. No. 5 Angelique Kerber was a 6-2, 6-4 victor over Elina Svitolina, overcoming four dropped service games, and sixth-seeded Li Na defeated Sesil Karatantcheva 6-1, 6-3 without dropping serve.
Other seeded winners Monday included No. 9 Samantha Stosur, 11th-seeded Marion Bartoli and 15th-seeded Dominika Cibulkova. Also advancing were No. 18 Julia Goerges, 19th-seeded Ekaterina Makarova, 22nd-seeded Jelena Jankovic, No. 23 Klara Zakopalova, No. 27 Sorana Cirstea and 30th-seeded Tamira Paszek.
Unseeded winners, in addition to Pervak, were: Madison Keys, Maria Joao Koehler, Stephanie Foretz Gacon, Misaki Doi, Vesna Dolonc, Kristyna Pliskova, Valeria Savinykh, Zheng Jie, Olga Govortsova, Irina-Camelia Begu, Alize Cornet, Heather Watson, Chan Yung-Jan, Romina Oprandi, Kirsten Flipkens and Lucie Hradecka.