Kartal, playing in only her third tournament since returning from six months out with a back injury, seized her first match point opportunity to complete a hard-hitting 6-2 2-6 6-4 win on Friday.
Her win means the 24-year-old, who made her breakthrough by reaching the fourth round of last year's Wimbledon, advances to the last four of a WTA 1000 event for the first time.
"I definitely did not think that I would find this level this fast. I think it's a bit of a surprise to me," said Kartal.
"I've had my best wins in my third tournament back. I did lose six months on the tour, but I don't feel like that when I'm playing on the court.
"Now that I'm back, I'm just going to try and maintain this level and try and find my ceiling and see where I can get to in the next year or so."
Kartal won two matches on her return to the tour at the China Open in Beijing earlier this month and has stepped up her eye-catching return with wins over ninth seed Belinda Bencic and former Wimbledon finalist Jasmine Paolini in Wuhan.
Kartal will play Jelena Ostapenko in the semi-finals after the Latvian outlasted 11th seed Diana Shnaider 7-6 (8-6) 6-1.
Seventh-seeded Iga Swiatek continued to make good progress, defeating American Ann Li, the conqueror of Aryna Sabalenka earlier in the tournament, with a 6-4 6-1 win that earned her a last-four date against French Open finalist Maja Chwalinska, who beat Maria Sakkari 6-0 3-6 7-5.
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