But, like last year, there was some streakiness - last year Kerber went up 61 31 before Li stormed back to win, 16 63 61, and this year Li stormed out to a 64 40 lead, Kerber won four of the next five games to close to 64 54, then the No.5-seeded Li finally shut the door on the No.9-seeded Kerber, 64 64.
Li had played into the night the night before, winning her second round match against Lauren Davis.
"I felt okay today," Li said. "Yesterday I played a three set match, and afterwards the physio was asking me how I was feeling, and I was saying, 'No problem at all. I can play another three sets, no problem.' Two sets today was pretty short compared to that, so I'm feeling good about everything right now."
"I'm very sorry that I have to withdraw from the tournament," Radwanska said. "Unfortunately, my granddad passed away last Sunday. The funeral is going to be Saturday, and I need to be there. I am disappointed to not continue with the tournament, especially because of my form so far this week.
"It was a difficult decision, but I need to go home and be with my family."
And so, Li - the defending champion at the Premier-level tournament - advances to the semifinals.
The other quarterfinal in the top half of the draw will pit No.1 seed Serena Williams against Simona Halep. Halep was the first to advance, pulling off a 64 46 62 upset over the No.11 seed, Sam Stosur; Williams won through in the night match, blasting seven aces during a 64 61 win over Mona Barthel.
"It definitely wasn't easy," Williams said of Barthel. "She's an interesting player. She seemed so light and smooth out there. You don't expect a ball to come that hard, but it was really hard, so that was a little bit surprising. But once I got used to it, it was a little better. I just had to get used to it today."
Williams didn't know too much about the German going in, but had seen her play. "I've always wanted to play her," she said. "She does well and I've seen her have some good results. I didn't know much about her before the match, but I knew her name. And she handled it well today. It was impressive."
Williams has beaten Halep in both previous meetings. The first one was close, with Williams winning in three sets at Wimbledon two years ago; the second one was not close, Williams going down an early break but winning 11 of 12 games from there to win in the semifinals of Rome this year, 63 60.
"Simona's a really good player," Williams said. "She gets so many balls back. I think she'll be tough for me on this surface. She plays so well. She's really fast, and she doesn't do anything badly.
"Those are opponents that sometimes can be the toughest to play."