US Open champion Coco Gauff was scheduled to face three-time major runner-up Ons Jabeur of Tunisia in the other singles match on Monday.
Swiatek, who won the French Open in June for her third grand slam title, is ranked No.2 and has a chance to overtake Aryna Sabalenka at No.1, depending on their results at the season-ending championships in Cancun, Mexico.
Left-handed Vondrousova, the reigning Wimbledon champion, broke in three of Swiatek's initial four service games en route to a 5-2 edge. Swiatek had trouble finding her range on the temporary outdoor hard court that has drawn criticism from some players at the event: She was responsible for 13 of the match's first 16 unforced errors.
Vondrousova served for that set at 5-2 and 5-4, but the Pole began turning things around and grabbed 13 of 17 points in one stretch. What became a four-game run put Swiatek ahead 6-5.
At 3-all in the tiebreaker, Swiatek took over for good. She smacked a big forehand winner, collected a service winner and hit her first ace of the evening to get to set point, before Czech Vondrousova double-faulted to end it.
That set took 64 minutes. The second lasted just 35, with Swiatek holding a 27-9 edge in points.
"I was 5-2 up and she started to play better," Vondrousova said.
"She didn't give me much of a chance after. The second set, she was playing really amazing - there was nothing much to do."
