Schiavone posed much more of a threat than their ranking disparity would suggest - the Italian, now ranked No.59 in the world, had a 4-3 lead in her head-to-head series with the World No.4. And in the middle of the match she did win five of seven games - but Radwanska didn't look troubled at all by that stretch, and the tournament's No.1 seed moved comfortably through to the quarterfinals, 64 63.
"It was a tough match out there," Radwanska said. "It was my first match back on hardcourts and the conditions were tough too, with the balls really flying here. And the serve was not the key in this match at all - we were both struggling with that - so I had to find a way to win without the serve today.
"It's also tough to play against somebody who plays such different tennis than the other girls - a lot of spin, one-handed backhand, slice - it's uncomfortable tennis to play against. It's always fun to play against Francesca, though the first few times I played her I really struggled to get used to it."
Radwanska's sister, Urszula Radwanska, is also still alive in the draw, playing her second round match on Thursday. How does big sister feel when she watches little sister grinding it out on the court?
"Well I'm very, very nervous all the time. When I'm somewhere else and watching her, for example on TV or on the live scores, I can't even watch, because I'm getting so nervous, even more than when I'm playing myself. But she has really been working hard the last couple of months and she's playing a lot better now, so she really deserves a high ranking and I'm really hoping she keeps doing well."
Next for Radwanska is No.6 seed Varvara Lepchenko, who beat Tamira Paszek, 64 64. Lepchenko had a tough time closing it out, finally winning the match on her seventh match point - it was a similar situation to her first round match on Tuesday, where she needed six match points to close it out.
"I don't know what it is about me these last couple of days, but hopefully it'll change!" Lepchenko said afterwards. "I've been thinking to myself, 'I really don't want to lose this set and then play three sets.'
"I really have to change my state of mind for the next match."
But even if it goes to a third set, the American has a secret weapon. "Physically I'm feeling great," she said. "I had some good fitness sessions the past three weeks, and that's a big key right now."
Radwanska has beaten Lepchenko in all three previous meetings, though they've all been competitive.
The only other second round match of the day saw No.5 seed Sorana Cirstea beat American qualifier Coco Vandeweghe, 63 63. Both players had done very well here last year, Cirstea making the semifinals and Vandeweghe making the final - and both were taken out by Serena Williams.