The No.12-seeded Cibulkova was the first of the pair to advance, outslugging No.8-seeded Petra Kvitova in straight sets, 63 62. Cibulkova fought off all five of Kvitova's break points during the match.
"I played really well today," Cibulkova said. "I was returning well and I was just very solid from the groundstrokes. She always goes for short points and quick rallies with her serve and first shots, but I hung in there and kept up with her in the rallies, and I'm really glad I could make it through today."
The No.1-seeded Li joined Cibulkova in the quarterfinals in the last match of the day, beating Aleksandra Wozniak, 61 64. The scoreline looked routine, but the ending was anything but - serving for the match at 61 54, Li needed 11 match points in a marathon 10-deuce game to close the match out.
"I think all the match I was feeling pretty good, except the last game!" Li said. "The funny thing was that in the beginning of the game I was feeling tight, nervous, and then I was like, 'What's going on? Why can't I finish the match?' And she wasn't giving up, and was defending so well. It was really tough.
"All I can say is wow, she saved a lot of match points. She's pretty good."
Despite the slight hiccup at the end, Li was pleased with her overall performance - and the result.
"At least I'm still in the tournament," she told reporters. "At least now I can still be in this press conference! Well, if I lose I can still be in here, but of course it would feel a little different."
"The last win didn't mean anything because I see she's playing well here," Li said.
"Hopefully I can get some revenge," Cibulkova said. "Actually I hope to finally just beat her. I've never beaten her before. I'll go on the court and use my experience from the Australian Open final.
"But she was playing really well that night - my game just wasn't enough."
The first two quarterfinals of the BNP Paribas Open - Simona Halep against Casey Dellacqua and Agnieszka Radwanska against Jelena Jankovic - will take place on Wednesday. The quarterfinals between Li against Cibulkova and Sloane Stephens against Flavia Pennetta are on Thursday.