Defending champion Swiatek eases into US Open second round
Swiatek, whose grip on top spot is under threat from Aryna Sabalenka in New York, needed just 58 minutes to dispose of the 86th-ranked Peterson.
The Pole broke her opponent five times and hit 20 winners to just two for Peterson, beaten in round one at the US Open for the fourth year running.
"I wanted to start the tournament with everything I was focusing on. I was happy to play a great game, with all the pressure and expectations I was happy on the court," said Swiatek.
"I feel like everything that is going on around us it is taking away our attention and what we want to achieve with our games and careers.
"I want to remind myself that I want to develop as a player. The numbers and stats don't really matter to me. I'm just trying to focus on my performance."
Swiatek, bidding for her fifth Grand Slam title, goes on to face Daria Saville of Australia in round two. She is now 18-1 in first-round matches at majors.
No woman has retained the US Open title since Serena Williams won the tournament three times in a row from 2012 to 2014.