Kvitova had the tougher day at the office, but luckily she had one of her very best serving days in a while - the No.3-seeded Czech fired 15 aces en route to a 76(2) 57 62 win over Lucie Safarova.
"I knew it was going to be a tough match - it's always tough when you're playing a friend, tough on the nerves," Kvitova said. "She plays aggressively like I do, and she has a good serve too, a lefty serve - whenever I play her I know how my opponents feel against me, and that's not a very nice feeling!
"I needed some games to get used to her game but I was able to keep coming back to win the first set, and in the third I felt like Lucie was a little bit tired. So I just took my chance to win the match."
And what about that serve? "I served well, yes," Kvitova added. "I had one window when I did some double faults, but I was really glad with the aces. I didn't see my first serve percentage yet."
The No.2-seeded Radwanska was in a little bit of trouble - a 4-1 first set lead became 4-all before she closed out the first set, 6-4, and she then dropped serve in the first game of the second set - but Croatian qualifier Mirjana Lucic-Baroni had to retire in the next game with a low back injury.
Apart from No.1 seed Li's departure at the hands of Czech qualifier Petra Cetkovska, which you can read more about here, it was actually a perfect day for the seeds, with No.4 seed Sara Errani coming back from 62 20 down to beat Monica Niculescu, 26 75 61; No.5 seed Jelena Jankovic beating Russian wildcard Alisa Kleybanova, 61 62; No.6 seed Angelique Kerber beating Klara Zakopalova, 62 63; and No.7 seed Simona Halep wrapping things up under the lights with a 64 61 win over Annika Beck.
Rounding out the final eight was Yanina Wickmayer, who followed up her second round win over No.8 seed Caroline Wozniacki with a streaky 16 62 60 win over Jana Cepelova. Cepelova was up a set and a break at 61 21 and started the next game off with an ace, which must have woken Wickmayer up big time - the Belgian won the next 11 games in a row against the Slovak to advance to the quarterfinals.
As for Li, she doesn't leave empty-handed - regardless of how she did this week she was going to rise to No.2 in the world next week anyway, a personal best and the highest ranking ever for an Asian player, male or female. And it wasn't Cetkovska's first Top 3 win, nor her first win against Li.
Still, a 3-1 third set lead with a point for 4-1 - and 11 double faults - may be tough to assess.
"I don't think I played so badly, but maybe I made some wrong choices that made me lose a lot of points, important points," Li said. "It doesn't matter if you're 3-1 up, or even 5-1 up, if you can't finish the match, your opponent always has a chance to win. I just wasn't able to hang in there today.
"But at least I was fighting on the court, and losing a match isn't just a bad thing, because you can learn a lot. I have some pretty good information now, so I'll start training and will improve for next time."