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Karolina Pliskova became the first woman to advance to the last four of the tournament.
The Prague tournament - played among the top Czech men's and women's players but without fans and with ball boys and girls wearing gloves and face masks - was one of the first after professional tennis was suspended in early March.
Fourth seed Sofia Kenin claimed her maiden French Open semifinal spot as she fought to a 6-4, 4-6, 6-0 victory over fellow American Danielle Collins.
Swiatek became the youngest player to reach the French Open women's final in 19 years when she crushed Argentine qualifier Nadia Podoroska 6-2, 6-1.
Kvitova struggled with unforced errors but still had enough weapons to defeat American Jessica Pegula 6-4, 6-3.
Thrashed 6-1, 6-4 by Kvitova last year, top seed Barty rode on a wave of crowd support as she defused the twice Wimbledon champion's power game before running away with the contest.
The Czech player has been replaced in the draw by lucky loser Kaja Juvan of Slovenia.
The Japanese world No. 3's place in the tournament will now be taken by alternate Kiki Bertens of the Netherlands.
The match at Rod Laver Arena was riven with tension, with a delay to close the roof during the first set due to the stifling conditions.
The two-time Wimbledon champion suffered severe wounds to her left playing hand as she struggled with the intruder in her flat during the attack in December 2016.
Results 11-20
