The 22-year-old Pole defeated Sweden's Rebecca Peterson 6-0, 6-1 in the first round of the women's singles at Flushing Meadows on Monday.
The Polish tennis star, who is the defending champion in New York, next takes on Australian Daria Saville for a place in the third round.
Świątek last month defeated Germany's Laura Siegemund 6-0, 6-1 in the final of the Poland Open tournament on home soil in Warsaw, claiming her 15th career singles title.
The Polish player, coached by countryman Tomasz Wiktorowski, has topped the world rankings in women's tennis since April 4, 2022.
The 2023 US Open began on Monday and runs until September 10.
(gs)
Source: Eurosport, PAP