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.
Boston schools pull out free condoms over wrapping complaints
Millions of Getty images now available for free via embed tool