It was the 28th time lucky for Svitolina, who came from a break down in both sets and survived a wobble as the finish line approached in the second.
She took a 5-2 lead in the second against the Czech, who was rebounding after a three-hour marathon match on Monday against Karolina Pliskova.
Svitolina prevailed though after just over an hour and a half in a match that included 10 breaks of serve.
Svitolina had lost her previous four Grand Slam quarterfinals, including at this year’s Australian Open, while her previous best result at Wimbledon was reaching the fourth round in 2017.
The 24-year-old advances to her first Grand Slam semi-final of her career.
“It feels amazing. It is the first semi-final for me, and I actually didn’t expect it to happen here. It is exciting and I am looking forward to it already,” the beaming 24-year-old said after setting up the last-four clash against former world number one Simona Halep.
“I had to fight for every point, take my chances, and just try to get the extra ball over the net.”
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