Two-time Wimbledon champion Kvitova lost to Aryna Sabalenka in the 2020 final, but has looked on top form throughout the week in Doha.
Kontaveit proved a tough opponent for the fourth seed, however, and Kvitova – the 2018 champion – needed three sets to progress 6-3, 3-6, 6-2.
“I’m really glad that after losing the second set, which I probably didn’t play the best, I started very well in the third,” said Kvitova.
“I learned that the return was pretty good from my side. I was going for it – first point, first shot – and I think that made a big difference. In the rally, it was 50-50 and anybody could win it, but when I put the pressure from my return, it was really very nice.”
— Petra Kvitova (@Petra_Kvitova) March 4, 2021
Her reward is a semifinal tie with qualifier Jessica Pegula, who caused an upset by defeating second seed Karolina Pliskova 6-3, 6-1.
Pegula reached the Australian Open quarterfinals last month and played with supreme confidence to oust the 2017 champion and reach her maiden semifinal at a WTA 500 event.
The other half of the draw will see Victoria Azarenka taking on Garbine Muguruza.
— Qatar Tennis Federation (@QatarTennis) March 4, 2021
Azarenka triumphed 6-2, 6-4 over top seed Elina Svitolina, with the two-time Doha champion maintaining her unbeaten record against the Ukrainian to reach the 60th WTA semi-final of her career.
Muguruza, meanwhile, battled past Maria Sakkari 6-3 6-1 to complete the last four.
At the Lyon Open, French duo Kristina Mladenovic and Clara Burel booked their places in the last eight, beating Margarita Gasparyan and Aliaksandra Sasnovich respectively.
Spaniard Paula Badosa awaits Mladenovic, while teenage wildcard Burel takes on compatriot and second seed Fiona Ferro in what is her first WTA quarter-final.
There were also victories for Greet Minnen and Viktorija Golubic.
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