No. 3 seed Dominika Cibulkova also advanced past the second round.
Radwanska defeated Daniela Hantuchova 7-6 (7-3), 7-6 (7-3) to set up a quarterfinal meeting with Cibulkova, who got past Stefanie Voegele 7-6, 7-6 (7-5).
Agnieszka Radwanska, ranked fourth in the world and seeded No. 1 in this event, was already assured a quarterfinal berth thanks to her second-round win Wednesday.
The Radwanska sisters are on opposite sides of the draw and can only meet in the finals. They have played on four occasions with Agnieszka holding a 3-1 advantage.
In other second-round matches Thursday, fourth-seeded Jamie Hampton won over Nicole Gibbs 7-5, 6-7 (5-7), 6-3 and Vera Dushevina eliminated Madison Keys 7-6 (7-0), 6-2.
Celebrity Breakups and divorces of 2014 [PHOTOS]