The match felt all but over for Kasatkina when Swiatek saved two break points and pounded a forehand winner past the Russian's outstretched racket for a 3-0 first-set lead.
The Pole cruised from there on, dominating with her serve, including one on match point that Kasatkina could not handle, to improve her head-to-head record against Kasatkina to 5-0 this year.
"I think I started pretty well and that gave me a lot of confidence," Swiatek told Tennis Channel.
"But on the other hand you have to be really careful and patient against Dasha. I wanted to play in a really solid way but put pressure on my opponent.
"I did that pretty well and I'm happy about it."
The win continues a phenomenal season for Swiatek, who rose to world number one in April and has won eight titles including two Grand Slams at Roland Garros and Flushing Meadows this year.
WTA Finals debutante Kasatkina has also raised her level this season, making the semi-finals of the French Open and returning to the top 10 for the first time since 2019.
See stats from the contest at Flashscore
The WTA Finals features eight women split into two groups, with the top two finishers moving into the semi-finals of the indoor tournament played on purple hard courts in Texas.
In the other Tracy Austin group match of the day, France's Garcia beat American teenager Gauff 6-4 6-3 to get off to a flying start.
The veteran Frenchwoman, who also triumphed over Gauff in the quarter-finals of this year's U.S. Open, was the better player on the match's biggest points, breaking an error-prone Gauff four times.
"The most important thing today is I stayed really positive, really focused on the present moment," Garcia, who faces Swiatek on Thursday, told Tennis Channel.
"We always know how important the beginning of the match is and I had an opportunity to win the first game but got broken, and I said like, that's not good. But I stayed positive and was able to stay calm."
American Jessica Pegula faces Tunisia's Ons Jabeur and Aryna Sabalenka battles Maria Sakkari in group stage action on Wednesday. The WTA Finals conclude on November 7th.
