Williams notched the first of her 11 2013 championships at last year's Brisbane tournament and started the latest edition with a solid 6-4, 6-4 showing over Andrea Petkovic in a second-round match.
Williams dropped her serve once early in the match but ended up winning about two-thirds of the points on serve. She was particularly strong in the second set, losing seven points over five games serving.
Fourth-seeded Jelena Jankovic advanced with a 6-1, 6-3 romp over Elina Svitolina in 60 minutes. Jankovic lost only eight points in eight games serving and didn't face a break point.
Dominika Cibulkova, the No. 8 seed, got by Kimiko Date-Krumm 6-3, 1-6, 6-3. Date-Krumm had six break chances in each set but Cibulkova fought off 13 of them. Cibulkova took the match with three third-set breaks.
Kaia Kanepi knocked out ninth-seeded Carla Suarez Navarro 6-2, 6-2, taking 60 percent of the points in the hourlong match. Kanepi had six breaks in eight receiving games.
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