Radwanska had her first-round match pushed one day from Tuesday because of weather and then wasn't able to finish the match Wednesday due to rain.
However, she started Thursday's play by winning three of four games to finish off a 6-2, 6-4 first-round win over Akgul Amanmuradova and then topped Karolina Pliskova 6-4, 6-4 in a second-round match.
Pliskova pounded out 14 aces but Radwanska had three breaks in moving to the quarterfinals.
Second-seeded Jelena Jankovic routed Jill Craybas 6-2, 6-0 in 65 minutes Thursday. Jankovic lost just 10 points over seventh service games. She won the first four games of the match and in the second set won two-thirds of the points.
No. 3-seeded Peng Shuai was a 2-6, 6-1, 6-4 winner over Kristyna Pliskova -- Karolina's twin sister. Peng didn't drop her serve after the first set.
Sixth-seeded Ayumi Morita defeated Misaki Doi 7-6 (8-6), 6-2 but Eleni Daniilidou upset fourth-seeded Jarmila Gajdosova 6-4, 6-0 and Olivia Rogowska got by No. 7-seded Jelena Dokic 3-6, 6-4, 7-6 (7-2).
Radwanska meets Hsieh Su-Wei and Daniilidou plays Rogowska in the top half of the draw's quarterfinals. Jankovic goes against Morita and Peng faced fifth-seeded Petra Martic in the other matches Friday.