Petra Cetkovska upsets Li Na
"She played well. I don't think I was playing so bad," Li said. "Maybe, sometimes the wrong choice made me lose a lot of important points."
It was the top-seeded Li's first loss of the year having won her two previous tournaments: Shenzhen and the Australian Open.
Regardless of her early defeat in Doha, Li will move up to a career-best No. 2 in the WTA rankings on Monday, overtaking Victoria Azarenka, who was not defending her Doha title because of a foot injury.
The left-handed Kvitova served 15 aces and took advantage of four of five break-point opportunities in the two-hour, 25-minute match.
"I served well, yes," said Kvitova, the 2011 Wimbledon champion. "I had one window when I did some double-faults, unfortunately. But with the aces I'm really glad."
In Friday's quarterfinals, Cetkovska plays Angelique Kerber, Radwanska takes on Yanina Wickmayer, Kvitova faces fifth-seeded Jelena Jankovic, and fourth-seeded Sara Errani faces either seventh-seeded Simona Halep or Annika Beck.
Li, playing her first tournament since winning the Australian Open, had a 3-1 lead in the third set, but the 133rd-ranked Cetkovska refused to fold.
"It's an amazing victory," Cetkovska said. "It's a little bit difficult to describe exactly what I feel at the moment.
"Even though I was 3-1 down in the third set I could manage to make it and get through."
Despite breaking Cetkovska's serve on six of 12 opportunities, and surrendering only three of her own service games in 11 break points faced, Li played tentative tennis throughout the two-hour, 46-minute match.
"It was cold. It's windy," said Li, noting the inhospitable weather greeting tennis players in Doha this week.
"The court is a little slower. When I think I can hit a winner the opponent always gets the ball back, so I always have to be ready for the next shot."
This marks the eighth time Cetkovska has beaten a top-10 player. It's only the second time she's beaten a top-three ranked player -- she upset the then third-ranked Agnieszka Radwanska at the 2011 Rome tournament.