Cibulkova, the 2013 champion, was ahead 5-2 in the first set before Radwanska rallied to tie it. Cibulkova, playing in her first match of the week after a first-round bye, cruised in the first-set tiebreaker and had no problems in the second set. She will face No. 5 seed Misaki Doi of Japan on Friday.
CoCo Vandeweghe, the No. 4 seed, rallied to beat Nicole Gibbs 2-6, 6-4, 6-2. Gibbs won the first three games of the match and cruised in the first set. But Vandeweghe got the first break of the second set for a 5-4 lead, won it on her serve and took the first three games of the third set.
Vandeweghe will face Alison Riske, who dropped the first five games of her match but rallied to beat qualifier Ana Bogdan 3-6, 6-2, 6-4.
CiCi Bellis defeated fellow American Sachia Vickery 4-6, 6-4, 6-3 and will face top-seeded Venus Williams on Friday night. Bellis, a 17-year-old wild card, broke Vickery in the seventh game of the third set, held serve in the eighth and broke again for the win.