Radwanska defeated Simona Halep 6-3, 6-1 in just more than an hour. Radwanska, now 3-0 lifetime versus Halep, lost 10 points on serve over eight games. Four of those points came in a service break.
She had five breaks against Halep, winning 57 percent of the points when receiving serve.
Johanna Larsson edged past Goerges 7-5, 6-7 (1-7), 6-3 by cashing her both of her break chances in the third set. She ended up taking 120 points, against 113 for Goerges, in the 2-hour, 32-minute match.
Third-seeded Yanina Wickmayer rolled to a 6-3, 6-0 rout of Romina Oprandi by taking more than 60 percent of the points in the match and eighth-seeded Mona Barthel topped Eleni Daniilidou 7-6 (7-5), 6-2 with five breaks in 10 receiving games.
But Elena Vesnina upset sixth-seeded Yaroslava Shvedova 6-2, 6-3. Shvedova hurt her chances with seven double faults and had her serve broken five times in nine games.
Other second-round results Wednesday saw Jamie Hampton defeat Marina Erakovic 6-1, 7-6 (7-5); Kirsten Flipkens oust Pauline Parmentier 6-2, 6-2 and Kiki Bertens beat Heather Watson 6-4, 3-6, 6-3.