"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).
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.
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 Kvitova.
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. She will face Danielle Collins.
Pegula, the eighth seed, ended the run of Chinese qualifier Yuan Yue, 6-2, 6-7 (6/8), 6-0.
Victoria 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.