Speaking on court after her victory, Kartal said she knew "what a great fighter" world number six Svitolina is, so she "was never safe" in the match.
"It was solid composure from me throughout," she added. "It's breaking new ground for me this week.
"I love playing here and on this court. The atmosphere was amazing, so big thank you to the crowd."
Kartal had not dropped a set during her run to the quarter-finals at Wuhan, and she broke Svitolina early in the first to start on a positive note.
Svitolina then called for a medical timeout for treatment on her right arm, but she came back strong to take the second set 6-2 and send the last-eight tie to a decider.
The two players were evenly matched in the third set but it was Kartal, using a protected injury ranking to play, who managed to break Svitolina's serve at 5-4 and book her place in the last four.
In the other quarter-finals, Polish 16th seed Maja Chwalinska faces Greek Maria Sakkari, while American Ann Li takes on six-time Grand Slam winner and seventh seed Iga Swiatek.