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Both players are recovering from injuries that kept them out of the Paris Olympics.
Vondrousova became the first female holder to fall at the opening hurdle since Steffi Graf 30 years ago.
Yastremska, the world No. 93 who reached the third round at Melbourne Park in 2019, secured the early break in the second set as her opponent continued to spray the errors and the 23-year-old held firm to seal the victory.
Swiatek completed the first set comeback on a double fault and a disillusioned Vondrousova went quietly in the second set.
The 24-year-old Czech rose 32 places to 10th in the new WTA rankings after winning her first Grand Slam title.
Results 1-5
