
The 18-year-old quickly went down 4-0 to outsider Kristina Kucova — the world number 317 who knocked out Jelena Ostapenko in the first round — before recovering to win 7-6 (8/6), 6-2.
“Even though I was losing 4-0 I had a fighting spirit and I knew that I would find my game if I stayed patient,” Yastremska said.
“The crowds were supporting me so I felt that energy and I was very motivated to come back.”
She added, “I was very nervous and I made a lot of mistakes, but I realised that I’m nervous and I just had to get through it.”
Earlier this year, the big-serving teenager became the first player born this millennium to break into the WTA top 100 rankings.
The 2016 Wimbledon girls singles finalist is currently ranked 102 and faces a semi-final against China’s number two Zhang Shuai or last year’s runner-up Daria Gavrilova.
Two-time Grand Slam champion Garbine Muguruza was on court against Thailand’s Luksika Kumkhum, while China’s Wang Qiang takes on world number five Elina Svitolina in the late match.