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 semi-finals earlier this month but showed no lack of vigour 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 the world number one since April 2022 as she whacked across an unreturnable backhand shot to break Peterson to love in the fourth game.
Peterson, who was 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."
Swiatek was having fun off the court too, taking in the Lion King musical to keep up her tradition of seeing a Broadway show during every trip to the year’s final major.