Williams had 13 of her 19 unforced errors in the opening set when the 76th-ranked Camerin traded crisp groundstrokes with the eighth-seeded American.

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But with the score tied at 5-5, Williams found her stride and won eight of the final 10 games.

"I feel like I played better than I did in my first match," Williams said. "But I'm still trying to get it to come together."

In her first round match, an error-prone Williams defeated Germany's Angelique Kerber 6-3 7-5.

The two-times U.S. Open champion had not played in a tournament since losing to Justine Henin in the quarter-finals of Wimbledon last month.

In the third round Williams will play Russian Vera Zvonareva, who knocked out Maria Sharapova from the Australian Open in the round of 16 earlier this year.