Both players have been beset by injuries and have plummeted in the rankings since being in the top 10 last year.
The 164th-ranked Vondrousova, who underwent a left shoulder operation last summer, will play either Belarus' world number one Aryna Sabalenka or 2022 Wimbledon champion Elena Rybakina of Kazakhstan in Saturday's semi-finals.
It will be Vondrousova's first last-four appearance since Stuttgart in April 2024.
"We've played many times, so I think we know each other," said Vondrousova.
"We have similar slices and drop shots - I think it was a great match today."
In the other half of the draw China's Wang Xinyu - conqueror of French Open champion Coco Gauff on Thursday - reached the semi-finals after Spanish opponent Paula Badosa retired having lost 6-1 in the first set.
Wang will play either last weekend's Queen's finalist Amanda Anisimova of the United States or Liudmila Samsonova, who has already beaten defending champion Jessica Pegula and Naomi Osaka this week.