One more win for each player will lead to a semifinal confrontation that will be their first match since the 2009 Tour Championship.
The sisters met five times in 2009, with Serena winning the last four -- including a showdown in the Wimbledon championship match. Serena holds a 13-10 all-time lead on her sister.
In other third-round matches Thursday, Vera Zvonareva rallied to defeat Stefanie Voegele 5-7, 6-3, 6-4; Nadia Petrova ousted Anastasia Pavlyuchenkova 6-1, 6-4; Polona Hercog fought off second-seeded Marion Bartoli 6-4, 1-6, 6-4; and Lucie Safarova ousted Aleksandra Wozniak 6-2, 6-7 (4-7), 6-1.
Swim Week Miami Beach 2014 [PHOTOS]