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."
Williams and defending champion Victoria Azarenka advanced Monday, losing just four games between them against Russian rivals. Williams beat No. 14 Maria Kirilenko 6-2, 6-0, and Azarenka defeated Elena Vesnina 6-1, 6-1.
On the men's side, No. 2 Roger Federer and U.S. Open champion Andy Murray stayed on course for a semifinal in their half of the draw.
Federer won 6-4, 7-6 (4), 6-2 over big-serving Canadian Milos Raonic, advancing to the quarterfinals at a Grand Slam for the 35th consecutive time, while Murray took advantage of Gilles Simon's fatigue for a 6-3, 6-1, 6-3 victory.
Federer will face 2008 Australian finalist Jo-Wilfried Tsonga, who beat friend and fellow Frenchman Richard Gasquet 6-4, 3-6, 6-3, 6-2.
Murray, who ended a 76-year drought for British men in Grand Slam tournaments with a win at the U.S. Open, will next play unseeded Frenchman Jeremy Chardy.
Chardy spent some time in the offseason hitting against Williams in Mauritius, and they're both saying it has helped his game.
Williams also played Stephens at the Brisbane International earlier this month, winning their quarterfinal 6-4, 6-3 en route to the title. That night, Stephens said, she "lost to the best player in the world."
But there were times in the match when the American teenager was cranky, particularly when Williams unleashed some loud and long "Come ons" to celebrate vital points.
Stephens, looking toward her coach at one point, said the celebrations were disrespectful.
Later, she said she was just joking.
Regardless, it was a lesson. The friendly Serena from the locker room is the ultimate competitor — she's on a 20-match winning roll and has lost only once since her first-round exit at the French Open.
"Obviously every match is a learning experience," Stephens said. "But, I mean, you've just got to go and treat it like another match."
Well, not exactly a normal match, she said, but certainly no different from playing any of the other top three players.
"It just happens to be Serena. She's obviously one of the greatest players to ever play the game," Stephens said. "Without the titles, with the titles, it's still a tennis match. The court's the same size. You're still playing a regular person across the net."
Stephens and Williams ran across each other in the locker room Sunday.
"She told me I was too quiet on the court," Stephens said. "Then today I was thinking to myself, 'I'm really loud. Should I tone it down a little bit?'"
Williams thinks she's more like an elder stateswoman for the younger U.S. players than mentor for the likes of Stephens.
"I just feel like being the older one ... maybe some of the younger players look up to me," she said. "It's hard to be a real mentor when you're still in competition."
And as the elder stateswoman, Williams said, "I feel no responsibility" when it comes to playing Stephens.
"I doubt she has any expectations of me to be responsible for anything," she said. "I'm here to compete and do the best I can, as well as she is. And she's been doing really amazing. I'm really happy. I have a tough match, so we'll see."
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