The world number one was not at her absolute best after a two-month break and struggled with the scorching temperatures, but could not have been happier with her form leading into the first Grand Slam of the year.
Russia's Dinara Safina also opened her new season with a win but had to work much harder before toppling Poland's Agnieszka Radwanska 7-5, 6-4 to advance to the quarterfinals.
Russia's defending champion Elena Dementieva beat Slovakia's Daniela Hantuchokova 6-2, 4-6, 6-2 while Victoria Azarenka of Belarus defeated Kimiko Date Krumm of Japan 6-1, 5-7, 7-5, leaving four of the original eight seeds in the women's draw.
The only high-profile casualty was Russia's French Open champion Svetlana Kuznetsova, who was beaten 7-5, 6-2 by Dominika Cibulkova of Slovakia.
Medina wins
Spanish top seed Anabel Medina Garrigues came from behind to beat Russian qualifier Alla Kudryavtseva 3-6, 6-3, 6-1 at the Hobart International on Tuesday. Medina Garrigues recovered from her slow start to run away with the match and set up a quarterfinal against Gisela Dulko, who beat Austria's Tamira Paszek 6-1, 0-6, 7-6.
Alona Bondarenko of Ukraine, the fourth seed, beat Alize Cornet of France 6-4, 3-6, 6-2. She will play Zheng Jie in the quarterfinals after the Chinese player beat compatriot Peng Shuai 6-2, 6-1, in the Australian Open warmup.
In Auckland, former champion Philipp Kohlschreiber beat first round opponent Inigo Cervantes-Huegun 6-2, 6-3 at the Auckland Open. Kohlschreiber plays Thomaz Bellucci in the second round after the Brazilian beat Marco Chiudinelli of Switzerland 6-3, 6-3 on Monday.
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