Swiatek, who has enjoyed a stellar year that included Grand Slam singles titles at the French and US Opens, eased to a 6-2, 6-3 victory in one hour and 22 minutes at Fort Worth's Dickies Arena in Texas.
The Pole is the heavy favourite to add to her tally of eight tournament victories at this week's eight-player tournament.
Against Kasatkina on Tuesday, the three-time Grand Slam champion was quickly into her stride, racing to a 3-0 lead after an early break of serve.
Swiatek wrapped up the first set in just 37 minutes after securing another break of serve in the eighth game.
The second set followed a similar pattern, as she grabbed an early break to take control for a 3-0 lead before closing out the set.
Swiatek is aiming to atone for her disappointing display at last year's finals, held in Guadalajara, when she failed to qualify for the semi-finals.
"I'm pretty happy that I could start so solid," Swiatek said of her win. "I feel like it gave me confidence throughout the whole match.
"I knew it was going to be hard to balance being aggressive and you know, not making a lot of mistakes, because she can really reset the rallies."
Swiatek said working to improve her service game had been the key to her season of success.
"I felt like sometimes last year, my serve was letting me down," she said.
"And this season I can lean on it. Maybe it's not like I'm serving aces, but I feel more solid."
In Tuesday's other group game, France's sixth-seed Caroline Garcia defeated fourth-seed Coco Gauff in a repeat of their US Open quarter-final in September.
Garcia, who reached the semi-finals at Flushing Meadows before losing to Tunisia's Ons Jabeur, took one hour and 18 minutes to defeat US hope Gauff 6-4, 6-3.
The tournament features two groups of four players who play in a round-robin format, with the top two in each group advancing to the semi-finals.
This year's tournament was moved to Texas amid ongoing pandemic-related issues with the Chinese city of Shenzhen, which was initially due to the host the event, as well as the WTA's dispute with China over the status of player Peng Shuai.
