Though both players have been at or around the top of the game for years, this was curiously only their second career meeting - and the first, all the way back during the clay court season in 2006, wasn't even a complete meeting, as Li won it when Ivanovic had to retire after losing the first set.
The players' lack of familiarity with each other was evident throughout the match as neither really grabbed a hold of any real momentum - Ivanovic stormed out to a 63 10 lead, then Li won six games in a row to sneak out the second set 6-1, then Ivanovic jumped out to a 5-2 lead in the third set.
But it was the last momentum swing that decided it, as the No.4-seeded Li won four of the next five games to push the third into a tie-break, eventually closing the No.16-seeded Ivanovic out there.
"I was surprised because she was playing so aggressive, and I didn't really have time to prepare my game plan," Li said afterwards. "At the start of the second set I began hitting the ball into the court more, though I was still hitting the ball, because if I played a little bit soft, she was attacking a lot.
"I was just trying to see if I could turn it around, and I'm happy I was able to. I was happy with how I played today - sometimes you can't play your best, but you just hang in there until the end."
"I played Sloane a few times before and it was always long and tough three set matches," Radwanska said. "I knew it was going to be tough. She's a very solid player, very consistent. She's not giving any free points. So we had lots of good rallies. It was a quick first set, but I think she started playing much better in the second set. Suddenly it was 1-4. I knew I had to start playing much more aggressively there, and especially in the end of the second set, and throughout the tie-break, as well.
"I had a couple of good shots in the important moments and was able to come back in that set."
Radwanska's overall thoughts on Stephens? "She's playing a lot of good matches against top players," she said. "I think experience is a lot. She's a very young Top 20 player and is playing really well.
"I think she can really be in the top for so many years."
Sara Errani, the No.5 seed, also had a battle on her hands against Alizé Cornet, originally leading 75 51 with match point at 75 52, but nearly getting pushed to a third as Cornet fought back to bring up a set point of her own leading 6-5; Errani would end up closing the Frenchwoman out, 75 76(3).
Radwanska and Errani will now play in the quarterfinals, with the World No.4 leading the World No.6 in their head-to-head series, 6-2, but it was Errani who won their only previous meeting in 2013.
"We always play long matches," Radwanska said. "We play a little bit similarly. That's why there's a lot of running and a lot of long rallies with us, and that's why I think our matches are always very long.
"And, well, for sure this one is not going to be short, either."