Swiatek began her title defence with an almighty comeback, rallying back from a set and a double-break down to overcome eighth-seeded Barbora Krejcikova 4-6, 7-5, 6-2 in two hours and 33 minutes.
The win was crucial for the Polish second seed to keep her hopes of wrestling back the number one ranking from Aryna Sabalenka alive.
Meanwhile, third-ranked American Gauff had a more straightforward evening, completing a 6-3, 6-2 win over her compatriot and US Open finalist Jessica Pegula in 75 minutes.
"She's always a tough opponent. And these conditions against her, it's tough," said Gauff, who snapped a three-match losing streak to Pegula.
"But overall, I think I'm just happy with how I played. Sometimes it was sloppy, sometimes it was great, but that's tennis. I thought we both were playing at a high level. I think I just was able to break through on some of the more important points."
Earlier at King Saud University Indoor Arena, making her first competitive appearance in two months, Swiatek fell behind 4-6, 0-3 before she mounted a successful comeback against Krejcikova.
"For sure it wasn't easy. At the beginning I felt a bit rusty but I'm happy I found a way to play a little bit more solid," said Swiatek, who finished the match with 10 aces.
"I tried to do the usual stuff that I do to control the ball a bit more because it was flying like crazy off my racquet.
"I knew I had this game in me, I just needed to find it. It was hard to be patient with that but at the end I'm glad I just kept it going and didn't think what the score was."
Swiatek, a five-time major champion, skipped last month's Asian swing and hadn't played a match since her US Open quarter-final exit in early September.
The 23-year-old Pole parted ways with her coach of three years Tomasz Wiktorowski and debuted her new partnership with Belgian coach Wim Fissette at these WTA Finals.
Krejcikova is ranked 13 in the world but claimed a place in Riyadh as one of the tour’s best eight players due to a new rule implemented this season that gives priority to a Grand Slam champion that maintains a ranking between nine and 20 over the eighth-ranked player in the race to the tournament.
Fightback
Swiatek stared down three consecutive break points in her opening service game. She saved the first two but overcooked a forehand, sending it long to get broken at the start of the match.
A costly double fault saw Krejcikova fall behind 0-40 but the Czech swept the next five points to get out of trouble and inch ahead 4-2.
Swiatek saved a set point with a good serve in the ninth game to hold but Krejcikova was unnerved as she comfortably served out the set to take the lead in 47 minutes.
The two-time Grand Slam champion looked on her way to a comfortable straight-sets victory when she went up 3-0 with a double-break in the second set, punishing Swiatek's second serve and benefitting from her opponent’s mistimed shots.
But that only sparked a fightback from Swiatek, who erased her deficit by grabbing the next four games to take the lead for the first time in the match.
Krejcikova double-faulted at a crucial moment, handing Swiatek two set point opportunities in game 12. Swiatek converted her second chance to clinch the set and force a decider.
That took the wind out of Krejcikova's sails as Swiatek quickly carved a 5-0 gap.
Swiatek got broken while serving for the match but quickly self-corrected, breaking Krejcikova in game eight to seal the win.
With Sabalenka's opening round win over Zheng Qinwen on Saturday, Swiatek will now need to win the title, while winning at least two round robin matches, in order to secure the year-end number one ranking.
