MELBOURNE — Li Na advanced to the Australian Open semifinals for the third time in four years, bringing fourth-seeded Agnieszka Radwanska’s 13-match winning streak to a shuddering halt.
The 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 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.
Li will play the winner of Tuesday’s 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.
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.’’
On the men’s side, No. 2 Roger Federer and US Open champion Andy Murray stayed on course for a semifinal in their half of the draw.
Federer won, 6-4, 7-6 (7-4), 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 will next play unseeded Frenchman Jeremy Chardy.