The four-time Grand Slam champion fired off 20 winners and four aces to set up a second-round meeting with Australian Daria Saville.
Swiatek said that her tank was "pretty empty" after losing in the Montreal and Cincinnati semifinals earlier this month, but she showed no lack of vigor as she opened her US Open campaign with an ace and blazed through the first set.
The Polish player showed only brief signs of vulnerability early in the second set, as she began to accrue more unforced errors and had to claw her way back from triple break point in the first game.
But she reminded the crowd at Flushing Meadows why she has been No. 1 since April 2022 as she hit an unreturnable backhand shot to break Peterson to love in the fourth game, amid a 10-point winning streak.
Peterson, who only produced two winners across the match, never regained her composure and Swiatek pumped her first after closing out the match with a scorching backhand down the line.
"I really wanted to play solid and start [the] tournament with everything that I focused on [in practice]," she said in on-court remarks.
"I just feel happy that with all the pressure and expectations I can just have fun on court."
Also Monday, former world No. 1 Caroline Wozniacki marked her return to Grand Slam action for the first time in more than three years with a 6-3, 6-2 win over Russian qualifier Tatiana Prozorova to set up a meeting with 11th-seeded Petra Kvitova.
Wozniacki is competing in her third tournament since returning to the tour after retiring in 2020 to start a family, but the Dane's vast experience shone through against the 19-year-old Prozorova.
"It feels amazing to be back," Wozniacki said. "Obviously I was very nervous coming out here, I haven't been here since 2019, and a lot has happened since then.
"It just feels amazing to have the chance out here on this big court, playing a night session and getting a win under my belt. It feels so special."
Masarova converted all three break point opportunities she had during the 87-minute encounter to secure her first career win over a top-10 player.
Haddad Maia, a semifinalist at Roland Garros, saved 11 of 15 break points across the match as Stephens suffered yet another early Grand Slam exit.
While Stephens was left to reflect on a miserable year at the majors, where her best showing was a fourth-round appearance at the French Open, Haddad Maia set up a meeting with Stephens' American compatriot Taylor Townsend.
After leveling the contest to one set all, Stephens could not absorb the Brazilian's firepower in the third set, where Haddad Maia sent over 20 winners.
"I was expecting a big battle," Haddad Maia said. "I knew that I had to work very hard and try to focus on my game."
The first round concludes Tuesday.
Reuters and The Associated Press contributed to this report.