Li, who beat Cibulkova to win her second Grand Slam title in January, dropped her first set in four matches while improving to 15-1 this year. Li is playing her first major tournament as the No. 1 seed.
"Not like before if I come here, maybe like No. 6 or No. 7 seed," she said. "But I think I am handling very well, so just continue."
Flavia Pennetta defeated Sloane Stephens 6-4, 5-7, 6-4 in a wildly uneven match affected by swirling winds in the third set from a dust storm outside the Indian Wells Tennis Garden. Pennetta advanced to a semifinal against Li. No. 2 seed Agnieszka Radwanska and Simona Halep meet in the other semifinal Friday.
Li rallied from a 5-1 deficit in the second set to close to 5-4 before Cibulkova called for her coach. After they huddled, the Slovak player held to even the match at a set apiece.
They traded breaks to open the third. Cibulkova survived a service game that went to deuce seven times and staved off four break points to tie it up 2-2.
"I'm disappointed I didn't win because I had my chances. These are chances you have to take with such a player," Cibulkova said. "My serve was just not there. Maybe I tried to go for too much. Her serve was much better than mine."
Li's ace gave her a 4-3 lead as she swept to the final three games and the victory.
Since adding the Australian crown to the French Open title she won in 2011, Li's popularity continues to grow. She has 10 million fans on Chinese social media, and she has noticed the increased attention at Indian Wells.
"Even like practicing the fans were watching," she said. "But I think I find more fans supporting my husband, not for me. Even we are practicing, working out, if he hit a winner, everyone was like so happy."
Stephens was the lone American woman left in the tournament, enjoying her best showing of the year so far. She appeared poised to move on after winning six straight games over the end of the second set and start of the third. She took a 3-0 lead with an early break of Pennetta.
But the Italian, who at 32 is 12 years older than Stephens, won six of the final seven games, breaking the American at love in one of those games. Pennetta served out the 2-plus-hour match, winning on her fifth match point when Stephens sprayed a backhand wide. One point during the final game had to be replayed after a paper napkin blew across the court.
In the men's quarterfinals, Alexandr Dolgopolov beat Milos Raonic 6-3, 6-4, ensuring the Ukrainian will rise to a projected No. 23 in next week's ATP Tour rankings. Already, he has made the biggest jump in the top 50, moving up 26 spots since the end of last year to No. 31 before the tournament began.
"Obviously if you're ranked 20, 30, 40 you're a good enough player. To get in the top 10 you just need all those small things to be together and to be solid," he said. "It's really small differences from the players that are top 10 and top 50. I don't think I changed a lot and it's working good; I'm staying healthy; I'm doing all the things I did but a little bit better."
Dolgopolov faces a semifinal matchup against either Roger Federer or Kevin Anderson, who played later. Dolgopolov improved to 6-2 against top-20 opponents this year, including his third-round win over top-ranked Rafael Nadal.
Raonic took out fourth-ranked Andy Murray in three sets in the fourth round, but he couldn't follow it up win a win over Dolgopolov in their first meeting.
Dolgopolov signed his shoes and tossed them into the crowd after his victory.
"If I need to run a lot on the match, like today I needed to defend well, and against Rafa I needed to run a lot, it's usually one pair of shoes for me for a match," he said. "If there is a hole in the middle of the shoe, I'm going to throw it out. It's better to give it to the people."