Appearing in New York for the first time as the world's top ranked player, Świątek looked the part, breaking Paolini's serve seven times and reeling off the last seven games to advance.

The Polish top seed is the favourite to win the year's final Grand Slam after she dominated the French Open in June and went on a 37-match winning streak that was snapped in the third round of Wimbledon.

But her sheen of invincibility began to crack at U.S. Open tune-up events, where she went 4-4 in her last eight matches before putting the field on notice with her complete game on a hot and humid morning at Louis Armstrong Stadium.

"I'm pretty happy with the performance, and I feel like I have better rhythm than in Toronto and Cincinnati so that's great," Świątek told reporters.

"I'm trying to enjoy that. In the first set I played pretty solid, but I needed to take it up to another level. I did that at the end and in second set, so I'm pretty proud of that.

"I feel like my level is just better. We'll see if I'm going to hold on to that," she added with a smile.

She is likely to face a more difficult challenge in the next round when she runs into Stephens, who battled back to see off Belgium's Greet Minnen 1-6 6-3 6-3 to the delight of the New York fans.

"I was just fighting as hard as I can and with your guys support, you pushed me through, so thank you," she said.

"Happy to get another win at my favourite tournament."