The top-seeded Williams breezed by Kirsten Flipkens in their third-round encounter 6-0, 6-3. It was the 39th win in 40 matches for Williams, who has seven tournament titles to her credit in 2013.
Rybarikova won her eighth straight match when Marion Bartoli retired with an injury in the second set of their confrontation. Rybarikova had won the opening set in a tiebreaker. She is coming off a tournament crown last week in Washington.
The meeting between Williams and Rybarikova in Friday's quarterfinals will be their first. The other quarterfinals will send Agnieszka Radwanska against Sara Errani, Dominika Cibulkova against Li Na and Petra Kvitova against Sorana Cirstea.
Radwanska reached the quarterfinals by downing Sloane Stephens 6-1, 7-6 (7-2) and Errani defeated Alize Cornet 7-5, 7-6 (7-3).
In other third-round matches, Cibulkova won over Roberta Vinci 6-3, 7-6 (7-4), Li eliminated Ana Ivanovic 3-6, 6-1, 7-6 (7-5), Kvitova was a 6-3, 6-3 winner over Samantha Stosur and Cirstea ousted Jelena Jankovic 6-3, 6-4.
2014: NFL Cheerleaders [PHOTOS]
Julius Randle breaks leg during NBA debut