NEW YORK -- Rafael Nadal breezed past Richard Gasquet to reach the US Open fourth round on Saturday while world number one Iga Swiatek also made the last 16 with a win over unheralded Lauren Davis.

Four-time US Open champion Nadal extended his winning record over his good friend to 18-0 when he stormed past the Frenchman 6-0, 6-1, 7-5.

"I increased a little bit the level today. That's important for me. When the tournament keeps going, I'm able to rise a little bit. I'm happy for that against a very good friend like Richard," said the 36-year-old Spaniard.

Second seed Nadal, aiming at his 23rd Grand Slam title, set up a last 16 clash with 22nd seed Frances Tiafoe of the United States, who beat Argentina's Diego Schwartzman 7-6(7), 6-4, 6-4 earlier in the day.

Swiatek of Poland was made sweat in her 6-3, 6-4 win over home player Davis as she had to overturn a 4-1 deficit in the second set.

"For sure it wasn't as smooth as in first and second round," Swiatek said. "I'm pretty happy I made it through and could close it in second set and come back. That was pretty important for me."

"For sure she played totally differently than most of the players, which threw me a little bit off the rhythm," the two-time French Open champion said about her rival.

Men's third seed Carlos Alcaraz downed American Jenson Brooksby 6-3, 6-3, 6-3 and will vie for a quarterfinal spot against Croatian 15th seed Marin Cilic who pulled off a 7-6(11), 6-7(3), 6-2, 7-5 victory against Britain's Daniel Evans in four hours.

Britain's Cameron Norrie, seeded seventh, beat 19-year-old Holger Rune of Denmark 7-5, 6-4, 6-1 to reach the second week of the US Open for the first time. The Wimbledon semifinalist will take on ninth seed Andrey Rublev from Russia for a place in the quarterfinals.

Rublev outplayed No. 19 seed Denis Shapovalov of Canada 6-4, 2-6, 6-7 (3), 6-4, 7-6(7) in over four hours.

Chinese qualifier Yuan Yue finished her US Open journey after losing to local favorite and eighth seed Jessica Pegula 6-2, 6-7(6), 6-0.

Despite the defeat, Yuan has already set her best record at a Grand Slam tournament by reaching the US Open third round this time.

Next up for Pegula is a round of 16 clash against Czech Petra Kvitova who fought past two-time Grand Slam champions Garbine Muguruza of Spain 5-7, 6-3, 7-6(10).

Another Chinese hopeful Zheng Qinwen was also stopped at the third round after losing to 108th-ranked Jule Niemeier of Germany 6-4, 7-6(5).