Kasatkina and Bencic into Adelaide semis, Kenin battles back in Hobart
Twice Wimbledon champion Kvitova was at her most erratic, spraying 42 unforced errors over the court, but still managed to save two match points and hold for 6-6 in the second set at the Australian Open warm-up.
"There was a hurricane in sight after losing the game after being just one point away from the win," Kasatkina admitted.
"With Petra, the score doesn't matter, you just have to be ready for everything. I'm really happy that I was able to keep my focus in the tiebreaker."
The hurricane never arrived and Kasatkina sealed the victory in the tiebreak to move on to a last-four clash against Spain's Paula Badosa, who later beat Brazilian Beatriz Haddad Maia 7-6(5) 7-5 in her quarter-final.
Kasatkina, a top 10 player four years ago before plummeting down the rankings and almost giving up the sport, said she was looking to maintain her consistency after finishing 2022 well and making a decent start to the new season.
"It's a rollercoaster, that why guys who can stay top 10 for 10 years, or the whole of their careers, it's amazing," she said.
"I feel myself to keep this level is so difficult. Once you get relaxed, everything goes away."
Later on Thursday, Swiss Olympic champion Belinda Bencic survived a second-set scare to beat France's fourth-seeded Caroline Garcia 6-2 3-6 6-4.
"The key was to hold my serve. We both served great, it's hard to return against her, sometimes it felt like Russian roulette," Bencic said.
Bencic will next face familiar foe Veronika Kudermetova, who saved five match points in a battling win over American Danielle Collins 4-6 7-6(5) 6-1.
"We go way back into the juniors, we know each other from then," Bencic said of Kudermetova, who she has faced nine times on the tour.
"It's good to know how she plays, but in every tournament there are different conditions, so it will be a different match, you can't really compare."
Sofia Kenin has experienced the ups and downs of tennis like few others since winning the Australian Open in 2020 and she continued to show signs of progress in the quarter-finals of the Hobart International.
Now ranked 143rd in the world after illness, injury and off-court issues blighted her last three seasons, the American came from behind to beat Ukrainian Anhelina Kalinina 4-6 6-3 6-0.
Kenin, who won the tournament in 2019, will play Elisabetta Cocciaretto in the semi-finals after the Italian saved two match points on her way to a 5-7 7-6(8) 6-4 win over American sixth seed Bernarda Pera.
"I just tried to keep on fighting," said the world number four, who returned from her latest injury layoff in August last year.
"Match-after-match I'm playing better and I'm just going to try to keep going."
