It is the fewest number of seeded women to reach the third round at Roland Garros since the number of seeds expanded to 32 in 2002.
Swiatek, who is looking to lift the Suzanne Lenglen Cup for the third time in four years, started strongly before briefly struggling on Court Philippe Chatrier. The world No. 1 picked herself up quickly to end American Claire Liu's campaign with a 6-4, 6-0 victory.
"It's not easy when you play with the wind and change sides to play against it. I'm happy I raised my level in the second set," said Swiatek, who turned 22 on Wednesday. "Patience is important, especially on clay."
Swiatek raced to a 3-0 lead, but she looked too much in a hurry and Liu pulled one of two breaks back as the Polish player briefly lost her focus. Liu leveled for 3-3 but dropped serve again as Swiatek bagged the opening set.
Gauff subdued Julia Grabher 6-2, 6-3 in a tricky second-round encounter to continue her charge toward a first Grand Slam crown.
Gauff, who lost to Swiatek in last year's final, faced an early test against the 61st-ranked Grabher but saved two break points before surging to a 5-1 lead and wrapping up the opening set without any problems.
The pair freely traded breaks early in a tense second set before the 19-year-old Gauff seized the advantage and wrapped up the contest on serve.
"It feels great. She's a tricky player," Gauff said on court. "I played her on hard courts earlier this year, and she gets a lot of height and depth on her balls ... and sometimes you don't know what to expect."
"I cannot say that here it's easy for me. It's still every match getting better and better," Rybakina said on court. "It was a bit slippery for me today. I don't know why."
She ought to be feeling cozy on dirt after winning the Italian Open, but the 6-foot Kazakh is banking most of her confidence on her height advantage.
"This is my good weapon," she said, "but at the same time, to move on clay it's not easy. It's always I need more to prepare and, of course, be more patient during the rallies."
The Australian Open runner-up hit 30 winners to Noskova's 16, though both players had 26 unforced errors. The Moscow-born Rybakina, who beat Brenda Fruhvirtova in the first round, will next face Sara Sorribes Tormo of Spain.
Day, who won the girls' title at the 2016 US Open, is ranked 138th and came through qualifying to make her Roland Garros main-draw debut. She beat French wild card Kristina Mladenovic in the first round.
Injuries and the coronavirus pandemic stalled Day's career, she explained.
"I tore my quad. I fractured my foot. I tore both labrums in my hip. So it was just a lot of bad luck, one thing after another," Day said. "Every time I tried coming back, it just felt like something else would happen."
Jabeur initially struggled to control Dodin's power game as the 26-year-old French world No. 122 attacked almost every ball, playing with considerable risk. While she made many difficult points, Dodin missed several easier ones, including two volleys, to send Jabeur 4-2 up.
Dodin's risky play did not pay off when another audacious crosscourt forehand flew wide to hand Jabeur the first set.
The pair then traded early breaks in the second set, but Dodin's errors gradually piled up as Jabeur clinched the contest on her third match point.
It is the third time in five years that no French player has made the third round of the women's competition.
"Really solid for her age. She did everything better than me today," said the 79th-ranked Parry, who made it to the third round at two majors last season. "She doesn't miss a lot. Like nothing. You never have an easy point. It's always a long rally."
Andreeva, who is the youngest player to win a match in the women's main draw at the French Open since 2005, has dropped just six games through two rounds.
Andreeva, who is ranked 143rd in the world, and Gauff have practiced together, but that won't mean much Saturday.
"The practice and the match is different, so I might also play different," Andreeva said. "I don't know. Who knows?"
Reuters and The Associated Press contributed to this report.