The top-ranked player wants to make history by becoming the first female French Open champion since Justine Henin in 2007.
And on the second day of action at Roland Garros, the Pole got off to a great start, winning 6-1 6-2.
It sets up a fascinating matchup with Naomi Osaka, a fourth-time major champion who is still recuperating from her maternity break.
Swiatek remarked to the Paris audience, “This feels like home.”
“Hopefully I’m going to be here as long as possible.”
Despite rain delaying much of the schedule on Monday, Ons Jabeur, Coco Gauff, and Marketa Vondrousova were also among the victors.
But Varvara Gracheva, a 23-year-old Frenchwoman, defeated Greek sixth seed Maria Sakkari 3-6 6-4 6-3.
The 27th-seeded Linda Noskova of the Czech Republic defeated British player Harriet Dart 7-6 (7-3) 6-4. The top-seeded Katie Boulter of the United Kingdom will play Paula Badosa of Spain on Tuesday.