The 22-year-old Briton overcame her Chinese opponent 7-5, 4-6, 6-3 in her first appearance at the French Open since 2022.
Raducanu said she felt "really proud" after grinding through against Wang in a topsy-turvy encounter, which featured 16 breaks of serve and lasted nearly two hours 45 minutes.
After requiring a medical break in the first set, the 2021 US Open champion revealed she had been feeling ill all day.
"I woke up and I felt really sick, to be honest," Raducanu said in her post-match press conference.
"I felt bad from the morning. I was just trying and fighting through that. It was really difficult.
"To have kind of come through that and overcome how I was feeling, I'm really happy."
Raducanu fell in the second round three years ago in her only previous appearance at the tournament, and will face a stern test if she is to better her Roland Garros record this time around.
She will meet four-time winner Swiatek in the round of 64, after the Pole swept through 6-3, 6-3 against Slovakian Rebecca Sramkova.
"I think it's a match for me where I can really test and challenge myself," said Raducanu of her next opponent.
"I think exposure to the top players is great for where I'm at for my development.
"It's a match where I can... go for my shots, because I know if I just push the ball, I'm probably going to get eaten."
Swiatek holds a 4-0 record over Raducanu, with her most recent victory a bruising 6-1, 6-0 win in the third round of the Australian Open in January.