Sixth-seeded Li, who lost the 2011 Australian Open final to Kim Clijsters only months before her Grand Slam breakthrough at the French Open, had a 7-5, 6-3 victory over Radwanska in Tuesday's first match on Rod Laver Arena.
"She's a tough player. I was feeling today against a wall," Li said. "She can hit everywhere, but without a mistake. I was feeling just very tough. You have to focus on every shot. Not every point, every shot."
Radwanska came into the Australian Open with titles this season at Auckland and Sydney, where she beat Li in the semifinals, but continued her poor conversation rate in Grand Slam quarterfinals. She's only advanced further once in seven tries — at Wimbledon last year, when she lost the final to Serena Williams.
Sixth-seeded Li will play the winner of Tuesday's later all-Russian quarterfinal between No. 2-ranked Maria Sharapova, who conceded only five games in her first four matches at Melbourne Park, and Ekaterina Makarova.
"At least now I'm in the semis," Li said. Sharapova, "has to play, so... Right? Now I can start now to enjoy my day. She has to fight, yeah. So that's better."
The quarterfinals on the other half of the draw will feature American teenager Sloane Stephens against Serena Williams, who is aiming for a third consecutive major title, and defending champion Victoria Azarenka against two-time major winner Svetlana Kuznetsova.
Stephens has heard a lot of advice from Serena Williams. Pointers on her groundstrokes, and even on her grunts.
It's been mostly gentle encouragement, occasionally spiced with headline-making comments from Williams, who has predicted the 19-year-old American will one day top the women's rankings.
As Stephens learned earlier this month, though, it's one thing to play with Williams, another to play against the 15-time Grand Slam champion.
With a comeback 6-1, 3-6, 7-5 win over Bojana Jovanovski on Monday, Stephens qualified for her first quarterfinal at a major tournament. Williams has already played at that level 34 times.
"It will be tough, obviously. It's quarters of a Grand Slam," Stephens said. "There won't be that, like, first time, 'Oh, my God, I'm playing Serena.' That's kind of out of the window now. So that's good."
In the men's quarterfinals Tuesday, No. 4 David Ferrer was playing fellow Spaniard Nicolas Almagro and top-ranked Novak Djokovic was playing Tomas Berdych in a night match.Suggest a correction