Azarenka's defeat followed the fourth-round exits of top-ranked Serena Williams and Maria Sharapova and leaves 2011 French Open champion Li Na as the only major winner remaining in the women's draw.
Radwanska next plays No. 20 Dominika Cibulkova, who won the last eight games in a one-hour, 6-3, 6-0 quarterfinal rout of No. 11-seeded Simona Halep. Li, a two-time finalist in Australia, will play 19-year-old Canadian Eugenie Bouchard in the other semifinal.
Radwanska played drop shots and slices from the baseline, forcing Azarenka to come forward and then lobbing or passing her. She hit touch volleys with calm precision, and instinctively anticipated Azarenka's shots.
She didn't fall into big-swinging rallies against the second-seeded Azarenka, either, continually mixing it up and saving the power for when she needed it.
"She was aggressive. She was making everything. She was guessing right," Azarenka said. "I was just playing a little bit too predictably.
"In the second set I managed to fight back. Third set, the first game was important. I let it go, like easily let it go. From there just couldn't get back to it. It was tough."
Radwanska was also safe on her own serve, dropping just two games in the two-hour match while breaking Azarenka six times. She hadn't beaten Azarenka in their last seven matches, and had only won three of their previous 13.
7:30 p.m., ESPN2