The No.2-seeded Li won first, beating Mirjana Lucic-Baroni, 61 62. Lucic-Baroni has had a Top 5 win - against Monica Seles in 1999 - but Li was just too dangerous on the return, breaking her in seven of her eight service games. Li even held three break points in the Croatian qualifier's only hold.
"It's always tough when you change to a new surface so I'm excited to win my first match on clay for the season," Li said after the match. "Mirjana plays flat, so I had to be prepared for that. And I thought it would be a tough match because she has a lot of experience, too - she's over 30, like me!
"I was happy I could play more aggressively and had the right game plan to win."
Li Vs Lucic-Baroni Video: Li Interview
The No.5-seeded Kvitova followed Li into the quarterfinals with a 26 76(4) 62 win over Julia Goerges. Goerges seemed to be cruising to victory leading by a set and a break at 62 10, even holding a few points to hold for 62 20, but Kvitova found her range from there and fought to win in three sets.
Li and Kvitova, the French Open and Wimbledon champions in 2011, will play each other for the fifth time. They are tied in their head-to-head, 2-2, and their last three meetings have all gone three sets.
Another quarterfinal match-up set up earlier in the day was Angelique Kerber against Yaroslava Shvedova. Shvedova advanced first, coming from 5-2 down in the first set and 3-1 down in the second set to beat Carla Suárez Navarro, 75 64; the No.3-seeded Kerber won the first eight games of her match against Anastasia Pavlyuchenkova, eventually closing it out after a tighter second set, 60 64.
Kerber, who served exceptionally during the match - she lost just 11 points in eight service games - had lost to Pavlyuchenkova in both of their previous meetings, this year in Brisbane and Monterrey.
"After losing to her twice before, I was set on beating her here at my home tournament," Kerber said. "I felt good and it was fun being out there on this court. I made sure I didn't let her get into the match, which was important, as she is a very dangerous player - that was obvious in the second set.
"It's so nice being here. The crowd is fantastic and the tournament organization is perfect, and that's why the players have been voting this tournament as our favorite tournament for years now. This is also the only tournament my whole family can come to - that makes me doubly motivated here."
Kerber Vs Pavlyuchenkova Video: Match Highlights
Shvedova beat Kerber in the pair's only previous meeting, though it was almost three years ago.
"I played her once but that was years ago," Kerber said. "I have to ask my coach about her, or maybe a few of the other players. She must be playing well if she got this far at a tournament this big."