Rafael Nadal defeated close friend Richard Gasquet for the 18th time to reach the US Open fourth round on Saturday as world number one Iga Swiatek made the last 16 for a second successive year.

Four-time champion Nadal took his record over Gasquet to a perfect 18-0 with a 6-0, 6-1, 7-5 victory to stay on course for a 23rd Grand Slam title.

In women’s singles, world number one Swiatek downed unseeded Lauren Davis 6-3, 6-4.

Swiatek came back from 1-4 down in the second set to reel off five successive games against the American who called a medical time out in the first set to have her blood pressure taken.

The 21-year-old Pole will face Wimbledon quarter-finalist Jule Niemeier of Germany for a place in the last eight.

Swiatek has now won three matches in a row for the first time since capturing her second French Open in June.

“It’s not like I lost confidence or something. I still know anything can happen on these tournaments,” she said.

Nadal has now won 34 straight sets against Frenchman Gasquet who he first played as a junior.

On Saturday, he was barely troubled, winning the first nine games of the contest before Gasquet got on the board.

Next up for the Australian and French Open champion is 22nd seed Frances Tiafoe for a place in the quarter-finals.

“He’s a great player, very charismatic, very fast,” said Nadal of the American.

Tiafoe made the last 16 for a third successive year by seeing off Argentina’s Diego Schwartzman 7-6 (9/7), 6-4, 6-4.

The 36-year-old Nadal showed no ill effects of the bloodied nose he suffered when he accidentally bounced his racquet into his face in the second round.

“It’s a little bit bigger than usual but it’s okay,” he joked.

- Alcaraz breaks shoe -

Carlos Alcaraz, widely-regarded as Nadal’s Grand Slam heir apparent, claimed a season-leading 47th win despite breaking one of his shoes.

The 19-year-old third seed defeated Jenson Brooksby of the United States 6-3, 6-3, 6-3 on the back of 46 winners.

Alcaraz, a quarter-finalist in 2021, managed to break one of his tennis shoes as he slid to reach a ball mid-match.

“It’s the third time that I have done this. As you can see, I do a lot of sliding,” he said.

Alcaraz next faces 2014 champion Marin Cilic who fired 26 aces and 74 winners in total past Britain’s Dan Evans in a 7-6 (13/11), 6-7 (3/7), 6-2, 7-5 win.

British seventh seed Cameron Norrie made the fourth round for the first time with a comfortable 7-5, 6-4, 6-1 win over Danish teenager Holger Rune.

He next faces Russian ninth seed Andrey Rublev who needed five match points to see off Canada’s Denis Shapovalov 6-4, 2-6, 6-7 (3/7), 6-4, 7-6 (10/7).

Petra Kvitova defeated ninth-seeded Garbine Muguruza after saving two match points.

Kvitova came through 5-7, 6-3, 7-6 (12/10) and will take on Jessica Pegula of the United States for a quarter-final place.

Two-time Wimbledon champion Kvitova said she had drawn inspiration from Serena Williams when the American legend saved five match points before eventually being eliminated on Friday.

“I watched Serena and it was amazing how she was saving match points, so I tried to do the same today,” said two-time US Open quarter-finalist Kvitova who next faces three-time runner-up Victoria Azarenka.

Muguruza’s defeat, her sixth in seven meetings against the Czech, left only four of the top 10 women’s seeds in the tournament.

Sixth seed Aryna Sabalenka, who made the semi-finals in 2021, brushed aside French qualifier Clara Burel, 6-0, 6-2 in just 68 minutes.

Pegula, the eighth seed, ended the run of Chinese qualifier Yuan Yue, 6-2, 6-7 (6/8), 6-0.

Azarenka eased past Petra Martic 6-3, 6-0 to set up a last-16 clash with 2016 finalist Karolina Pliskova who downed Olympic champion Belinda Bencic 5-7, 6-4, 6-3.

US Open results on Saturday (x denotes seed; players representing Russia and Belarus are banned from competing under the name or flag of their countries):

Men’s singles 3rd rd

Ilya Ivashka bt Lorenzo Musetti (ITA x26) 6-4, 3-6, 6-2, 6-3

Jannik Sinner (ITA x11) bt Brandon Nakashima (USA) 3-6, 6-4, 6-1, 6-2

Marin Cilic (CRO x15) bt Dan Evans (GBR x20) 7-6 (13/11), 6-7 (3/7), 6-2, 7-5

Carlos Alcaraz (ESP x3) bt Jenson Brooksby (USA) 6-3, 6-3, 6-3

Cameron Norrie (GBR x7) bt Holger Rune (DEN x28) 7-5, 6-4, 6-1

Andrey Rublev (x9) bt Denis Shapovalov (CAN x19) 6-4, 2-6, 6-7 (3/7), 6-4, 7-6 (10/7)

Frances Tiafoe (USA x22) bt Diego Schwartzman (ARG x14) 7-6 (9/7), 6-4, 6-4

Rafael Nadal (ESP x2) bt Richard Gasquet (FRA) 6-0, 6-1, 7-5

Women’s singles 3rd rd

Iga Swiatek (POL x1) bt Lauren Davis (USA) 6-3, 6-4

Jule Niemeier (GER) bt Zheng Qinwen (CHN) 6-4, 7-6 (7/5)

Petra Kvitova (CZE x21) bt Garbine Muguruza (ESP x9) 5-7, 6-3, 7-6 (12/10)

Jessica Pegula (USA x8) bt Yuan Yue (CHN) 6-2, 6-7 (6/8), 6-0

Victoria Azarenka (x26) bt Petra Martic (CRO) 6-3, 6-0

Karolina Pliskova (CZE x22) bt Belinda Bencic (SUI x13) 5-7, 6-4, 6-3

Danielle Collins (USA x19) bt Alize Cornet (FRA) 6-4, 7-6 (11/9)

Aryna Sabalenka (x6) bt Clara Burel (FRA) 6-0, 6-2

US Open last-16 line-ups (x denotes seed; players representing Russia and Belarus are banned from competing under the name or flag of their countries):

Men’s singles:

Daniil Medvedev (x1) v Nick Kyrgios (AUS x23)

Pablo Carreno Busta (ESP x12) v Karen Khachanov (x27)

Alejandro Davidovich Fokina (ESP) v Matteo Berrettini (ITA x13)

Corentin Moutet (FRA) v Casper Ruud (NOR x5)

Ilya Ivashka v Jannik Sinner (ITA x11)

Marin Cilic (CRO x15) v Carlos Alcaraz (ESP x3)

Cameron Norrie (GBR x7) v Andrey Rublev (x9)

Frances Tiafoe (USA x22) v Rafael Nadal (ESP x2)

Women’s singles:

Iga Swiatek (POL x1) v Jule Niemeier (GER)

Petra Kvitova (CZE x21) v Jessica Pegula (USA x8)

Victoria Azarenka (x26) v Karolina Pliskova (CZE x22)

Danielle Collins (USA x19) v Aryna Sabalenka (x6)

Zhang Shuai (CHN) v Coco Gauff (USA x12)

Caroline Garcia (FRA x17) v Alison Riske-Amritraj (USA x29)

Ons Jabeur (TUN x5) v Veronika Kudermetova (x18)

Liudmila Samsonova v Ajla Tomljanovic (AUS)