The No.2-seeded Radwanska looked in trouble early on against Sorana Cirstea, facing double set point while serving 4-5, 15-40 in the first set. But something clicked from there, as she not only held that game, but ran off nine games in a row - and 12 of the last 14 points of the match - to prevail, 75 60.
"She's definitely a great player, hitting the ball very hard and moving very well, and I was really in trouble in the first set today," Radwanska said. "But as each game went on I played much better, getting used to the conditions and getting used to playing outdoors, and I'm happy I won in the end."
Most of the favorites advanced to the third round, with No.4 seed Sara Errani beating Hsieh Su-Wei, 60 64, No.5 seed Jelena Jankovic beating Karin Knapp, 60 62, No.6 seed Angelique Kerber defeating Karolina Pliskova, 76(2) 64, and No.7 seed Simona Halep squeaking past Kaia Kanepi, 64 36 76(5).
Halep had to battle back from 5-3 down in the third set to hold off the huge-hitting Kanepi.
"It was a tough match. Kaia played really well. I'm very tired now!" Halep said. "When she had 5-3 in the third set I think I came back very well - I really tried to stay aggressive and hit the ball, just keep hitting the ball hard, and I think fighting a lot really made the difference in the end of the match."
There was room for a few upsets, though, most notably No.8 seed Caroline Wozniacki falling to Yanina Wickmayer, 64 75, despite serving for the second set. It wasn't just a rematch of their 2009 US Open semifinal, which Wozniacki won, but it was Wickmayer's first win in their seven career meetings.
"It means a lot to me, especially after coming out of a rough time - being sick in Australia - so finally beating her is really good," Wickmayer said. "It's always tough playing Caroline. She's a great competitor and gets so many balls back, so it's always a balance of keeping the ball in and being aggressive. But I think I mixed it up well and found the right balance against her this time."