The victory also extended a remarkable record for the Polish star. Swiatek is the only player, male or female, to have reached at least the third round at every Grand Slam tournament played this decade.
Her run now stands at 27 consecutive Grand Slams, stretching back to the 2020 Australian Open.
Swiatek was rarely troubled by Podoroska, although she had to fight off four break points while serving at 5-3 in the opening set. She quickly regained control and broke twice in the second set to move 5-1 ahead.
The world number eight then closed out the match on serve after just 71 minutes, finishing with a powerful backhand.
Swiatek said she feels more comfortable at this year's US Open after winning the Toronto title in August, her first final appearance of 2026.
"I'm here with better feeling than any other Grand Slam this year," Swiatek said. "Just trying to enjoy every day and improve the game every day."
The 25-year-old has already won six Grand Slam titles and is now chasing a second US Open crown. She will face either Marie Bouzkova or Harriet Dart in the third round.
Elsewhere, Naomi Osaka recovered from a second-set setback to defeat Katerina Siniakova 6-2, 5-7, 6-1.
The 13th seed produced 11 aces and won 78 per cent of her first-serve points as she booked her place in the third round. Osaka will next face Belgian Elise Mertens.
Mertens, the 23rd seed, also advanced after beating Uzbekistan's Maria Timofeeva 6-2, 7-6(5).
The Belgian has now reached the US Open third round eight times in the last nine years.