The top-ranked Williams won for the 44th time in 45 matches as she seeks her ninth championship of the year. She disposed of Mona Barthel 6-4, 6-1 and will face Simona Halep in the quarterfinals.
Halep outlasted Samantha Stosur 6-4, 4-6, 6-2 one day after becoming a footnote in tennis history by handing Marion Bartoli the final loss of her career. After falling to Halep in the second round, the 28-year-old Bartoli surprisingly announced she was retiring from tennis.
That announcement came one month after Bartoli won the Wimbledon title.
Azarenka downed Magdalena Rybarikova 6-3, 6-4.
In other third-round matches, Agnieszka Radwanska sailed past Elena Vesnina 6-0, 6-2, Li Na was a 6-4, 6-4 winner over Angelique Kerber, Roberta Vinci eliminated Sara Errani 6-4, 6-3 and Jelena Jankovic won over Sloane Stephens 3-6, 7-5, 7-5.
Radwanska will meet Li and Vinci will face Jankovic in the quarterfinals.