Unseeded Williams eased past fellow American Meilen Tu 6-2 7-5 and now meets France's Tatiana Golovin.
BBC: SPORT | Tennis | Petrova and Williams both advance
Two former champions - Anna Smashnova-Pistolesi and Meilen Tu - were also among first-round winners.
BBC: SPORT | Tennis | Pratt eases through
She will next play the winner of the match between fifth seed Meilen Tu and Jill Craybas that was suspended because of darkness after two sets.
BBC: Leon Garcia advances
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