Świątek began Tuesday’s first round match in a cautious fashion, before stepping up a gear to take the first set 6:3, news outlets reported.
The Polish number one seed came into her own in the second set, not letting Paolini, the world number 56, win a single game, as she cruised to a 6:3, 6:0 victory, her 51st of the season.
Świątek could now face the 2017 US Open champion, America's Sloane Stephens, in the second round on Thursday.
The Pole is looking to claim her second Grand Slam title of the year, having won the French Open in June.
Later on Tuesday, another Polish player, the world number 73 Magda Linette, was set for to play the 22nd seed, Czech Republic’s Karolina Pliskova, who reached the US Open final in 2016.
Meanwhile, in the men’s tournament, Poland’s world number 10 Hubert Hurkacz was due to begin his US Open run against Germany’s Oscar Otte.
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Source: onet.pl, polskieradio.pl