Sharapova got past Yung-Jan Chan 6-1, 7-5 in her first match of the 2007 grass-court Grand Slam tournament. Sharapova won the Wimbledon women's title in 2004.
Mauresmo, who missed much of the spring recovering from an appendectomy but still seeded fourth this year, faced just one break point and blitzing Jamea Jackson 6-1, 6-3.
Also Tuesday, third-seeded Jelena Jankovic was extremely sharp in a 6-2, 6-0 romp over Anne Keothavong while eighth-seeded Anna Chakvetadze dumped Angelique Kerber 7-5, 6-3 and No. 10-seeded Daniela Hantuchova needed just 40 minutes to eliminate Anastasia Pavlyuchenkova 6-0, 6-1.
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