With that, she became just the second Japanese woman in the Open era to record 80 Grand Slam singles wins, after Ai Sugiyama.
It is also the first time since 2018 that Osaka, who reached the semi-finals in New York 12 months ago, has reached the third round at all four Grand Slam tournaments in the same season.
“I just told myself that it’s an honour to play on this court, honestly,” Osaka said.
“I just want to keep playing in front of you guys if possible, so to keep fighting as best as I can.
“The energy from the crowd, it’s very lively and I have the experience of growing up here and playing on this court many times. It’s really fun.”
Swiatek, a six-time major winner whose sole US Open triumph arrived in 2022, had no such issues.
Poland’s 25-year-old former world number one defeated Argentina’s Nadia Podoroska 6-3 6-2 to set up a meeting with Czech player Marie Bouzkova, who earlier ended Briton Harriet Dart’s tournament.
However, American Madison Keys survived a huge scare as the former finalist saved five match points to come through a thrilling match against Hungary’s Anna Bondar.
After forcing a third set, Keys, the 22nd seed at her home slam, trailed the decider by a double break of serve.
She stayed alive after Bondar produced back-to-back double faults on her first two match points, and three more on her subsequent service game, before breaking again to level the set and eventually clinching a 10-point tie-break to win 5-7 6-4 7-6 (10-5).