Prior to facing the Czech qualifier, Li had not lost this year following her successes at the WTA tournament in Shenzhen and at the Australian Open.
In a largely evenly-matched encounter, new world number two Li laid the blame for her loss on her inability to win the big points - and the poor conditions which players have had to cope with.
"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 cold. It's windy. 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."
Cetkovska, who has now beaten a top 10 player eight times, said: "It's an amazing victory. 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."
Meanwhile, second seed Agnieszka Radwanska walked through to the quarter-finals after her third-round opponent Mirjana Lucic-Baroni retired with a lower back injury with the scores 6-4 0-1 in the Pole's favour.
Radwanska will now play Yanina Wickmayer for a place in the semi-finals.
Kvitova had 15 aces on her way to setting up a last-eight meeting with Jelena Jankovic.
"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."
Fifth seed Jankovic sealed her progress with a comfortable 6-1 6-2 win over Alisa Kleybanova
In Friday's other quarter-final, fourth-seeded Sara Errani faces seventh-seeded Simona Halep.
Qatar Open results
7-Simona Halep (Romania) beat Annika Beck (Germany) 6-4 6-1
Yanina Wickmayer (Belgium) beat Jana Cepelova (Slovakia) 1-6 6-2 6-0
2-Agnieszka Radwanska (Poland) beat Mirjana Lucic-Baroni (Croatia) 6-4 0-1 (Lucic-Baroni retired)
3-Petra Kvitova (Czech Republic) beat Lucie Safarova (Czech Republic) 7-6(2) 5-7 6-2
6-Angelique Kerber (Germany) beat Klara Zakopalova (Czech Republic) 6-2 6-3
4-Sara Errani (Italy) beat Monica Niculescu (Romania) 2-6 7-5 6-1
Petra Cetkovska (Czech Republic) beat 1-Li Na (China) 7-6(2) 2-6 6-4
5-Jelena Jankovic (Serbia) beat Alisa Kleybanova (Russia) 6-1 6-2
- Sports & Recreation
- Agnieszka Radwanska
- Czech Republic
- Angelique Kerber