The top-seeded Williams, a winner of seven tournaments this year, breezed past Francesca Schiavone 6-3, 6-2 after receiving a bye past the first round.
Williams will next meet Kirsten Flipkens, who eliminated Kiki Bertens 7-5, 3-6, 6-2. Flipkens defeated Williams' sister Venus in the opening round.
Rybarikova, who won the tour stop last week in Washington, reached the third round with a 6-4, 6-2 win over Varvara Lepchenko. Marion Bartoli will face Rybarikova after defeating Lauren Davis 6-0, 6-3.
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