Poland's 22-year-old Swiatek, the French Open winner and a four-time Grand Slam champion, took only 89 minutes to dispatch 19-year-old American Gauff, who won the US Open last month.
"In the second set, obviously, it got more tight," Swiatek said. "I was happy I stayed focused. I had plenty of chances in her first service games to break back, but I knew somehow I would use one of those chances."
The victory also boosted Swiatek's chances to overtake Australian Open champion Aryna Sabalenka for the year-end world number one ranking at the season-ending outdoor hardcourt event in Mexico.
Tunisia's Ons Jabeur beat Wimbledon champion Marketa Vondrousova of the Czech Republic 6-4, 6-3 in a rematch of the Wimbledon final in the night's other group-stage match.
The result meant Swiatek has not clinched a semi-final berth despite her 2-0 start.
In windy conditions, Gauff hit only six winners compared to 31 unforced errors while Swiatek hit 11 winners, half her number of unforced errors.
"I would say this match wasn't consistent, in terms of the level," Swiatek said. "So for sure adjusting to everything that happened was the most important thing."
Swiatek, a three-time Roland Garros champion and last year's US Open winner, improved to 9-1 all-time against Gauff, whose only triumph in the rivalry came in August's Cincinnati semi-finals ahead of her first major title at New York.
Swiatek, the 2022 year-end number one, also beat Gauff in their most recent prior meeting last month at a Beijing semi-final but the US teen was nursing a right shoulder injury.
Gauff could not become the first teen to win multiple matches at a WTA Finals since Serbian Ana Ivanovic in 2007.
Gauff netted a forehand to surrender the first break and a 2-0 lead in the opening set and Swiatek smashed a backhand shot on the baseline to break again at love for a 4-0 edge.
Swiatek hit a backhand volley winner for another break to claim the first set in 27 minutes.
Gauff broke for a 2-1 lead in the second set when Swiatek hit a forehand volley wide, her third unforced error of the game, and Gauff held in a dramatic 12-minute sixth game for a 4-2 edge.
Serving for the set, however, Gauff made four double faults in a row and was broken to 5-5, then broken again by Swiatek in the final game, netting a forehand volley on the final point.
"I'm happy that I could actually problem solve a little the way to win these last games," Swiatek said. "The key was maybe being confident and mentally not focusing on the score, but really just sticking with the plan that worked in the first set."
Sabalenka must defeat Elena Rybakina of Kazakhstan on Thursday in a group-stage rematch of January's Australian Open final to qualify for Saturday's semi-finals.
Sabalenka would clinch the year-end top spot by reaching Sunday's final.
