The Belarusian world number one will next face Germany's
Australian Open champion Azarenka outplayed her Polish opponent from the baseline, coasting through the opening set in 25 minutes and racing to a 5-0 lead in the second before being surprisingly broken.
Though fifth-seed Radwanska then held serve for the first time in the match, Azarenka served out to clinch a one-sided victory in just over an hour when her opponent netted a forehand.
The pony-tailed Belarusian clenched her right fist in delight as she looked at the players' box, having moved into joint second place in the all-time standings for the best start to a WTA Tour season.
Swiss Martina Hingis leads the way with 37 consecutive victories to launch her 1997 campaign while American Serena Williams, with 21 in 2003, and Azarenka are next best.
"I was really impressed with the way I played today," a beaming Azarenka said after improving her record to 9-3 against Radwanska. "I didn't expect to win that way. I'm proud how I fought hard and played winning tennis.
"I had very good motivation because I knew she's an excellent player, so I had to come up with a great match today.
"I was just really focused on every moment, on every point I played, on every ball I was striking. I didn't really think about the score," added the 22-year-old, who converted six of her 12 break points.
Kerber broke Li twice in the opening set and three times in the second, completing her first win over the Chinese in four career meetings when her opponent hit a backhand service return long.
"This is very special," said the 24-year-old Kerber. "She's a great player and I had nothing to lose tonight.
"My plan was to be aggressive, play my normal game and move very well," added the German, who saved two match points in her opening match against American Sloane Stephens and three in her fourth-round victory over American Christina McHale. "I am very happy to be in the semis."
Radwanska came into Wednesday's match with a 20-3 record for this season, all three of her defeats coming against Azarenka.
"She played very well today, just way too good," the 23-year-old from Krakow said. "She was hitting really well with pretty much no mistakes and making the winners from those shots I didn't really expect.
"I had some chances, but when you're not really taking those chances against good players, then you're going down. It was just her day."
Radwanska, a winner of eight WTA singles titles, took some consolation from her projected rise to a career-high fourth when the new rankings are issued on Monday.
"I didn't really expect that," she smiled. "From the beginning of the year, my first time at No. 6, then No. 5, and now No. 4, and it's only March.
"I'm very happy about that, of course. I'm just hoping that I can play some good tennis, especially in the Grand Slams."