But the marquee match tomorrow will be a showdown between Svitolina and former No. 1 Angelique Kerber.
Japan's Naomi Osaka, the next opponent for Svitolina, beat Anett Kontaveit of Estonia 6-2, 7-6 (7/5), while French fifth seed Caroline Garcia put out Ekaterina Makarova 6-4, 6-2. She is bringing a lot of balls back, playing good tennis, moving good.
"I'm happy that it was in two sets because before we had such a tough battles", she said.
"I thought it was long, I was lucky", Kasatkina said in her post-match interview. "She gave me this chance and I took it".
"I just stayed in the moment, I was fighting, waiting for my opportunity, trying to earn opportunities". That's pretty much it.
She is content with the way she is dealing with the pressure of defending her title.
"I think that I was playing quite good today".
Just one break decided the first set between Kerber and Pliskova.
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The Czech won the second set and survived a run of three consecutive breaks of serve in the third, taking a 4-3 lead over Suarez Navarro.
Both of them have been world number ones, but Kerber has added two Grand Slams to her trophy cabinet. I had some kind of weird games on my serve. 'I actually think I'm playing better and better as the matches go on, as the season is going on.
"I know how to play on the centre court". Muguruza then applied huge pressure and had three break points in the ninth game.
All the momentum was running in Kasatkina after the rollercoaster second set, and she perfectly took advantage of the situation as her forehands started to become a real threat towards Muguruza, who was misfiring in every rally.
Muguruza started stronger and needed just one break point to claim the first set in clinical fashion but her opponent showed incredible resolve to push the second set to a tiebreak. Kasatkina, despite not playing her best tennis, was displaying some world-class counterpunching skills to grab the win, but also remained solid behind her serves especially when winning 59 percent of points behind her second serves, as compared to just eight points all match for Muguruza. "Very hard match. I think she always plays very good against the top players".
"Congratulations to our four semi-finalists, who have performed so well throughout the week", said Colm McLoughlin, Executive Vice Chairman and CEO of Dubai Duty Free.
Svitolina has won 6 of 7 against the German winning the last 4 including a victory in the Dubai semifinals a year ago.
Nonetheless, Kasatkina proved too strong as her fantastic week at the Dubai Duty Free Tennis Championships continues, having defeated Agnieszka Radwanska and Johanna Konta, saving another two match points along the way, in the past few days.