Swiatek battled to a 6-2, 7-5 victory over Irina-Camelia Begu of Romania as the Pole, back where she captured a fourth French Open title last month, had the advantage of playing under the roof of Court Philippe Chatrier.
"I'm happy to get through. The atmosphere was a little bit different so I was a little more nervous," she said.
"But I have the chance to work on a few things tomorrow so my level can be higher in the second round."
After two breaks in a comfortable first set, the top seed had to retrieve a break in the second set to get to 5-5 before sweeping the next two games and secured victory when Begu double-faulted.
Swiatek, who only made the second round on her Olympics debut in Tokyo three years ago, will face either Diane Parry of France or Argentina's Nadia Podoroska for a place in the last 16.
Italy's Jasmine Paolini, easily defeated by Swiatek in the French Open final, also made the second round with a 7-5, 6-3 win over Romania's Ana Bogdan.
"It's great to come back here, it's a different kind of tournament when it's the Olympics," said Paolini.
"I really love to play for my country but I feel a little more pressure."
As Swiatek and Paolini were safely in the second round, the start of play on the outside courts was delayed by more than four hours.
In all 40 matches were scheduled to be played on the uncovered courts on the opening day.
