The two-time champion, who could meet old rival Roger Federer in New York for the first time at the semi-final stage, crushed Ukraine’s Alexander Dolgopolov 6-2, 6-4, 6-1.
The 31-year-old Spaniard goes on to face Russian 19-year-old Andrey Rublev, who stunned Belgian ninth seed David Goffin 7-5, 7-6 (7/5), 6-3 to become the youngest quarter-finalist in New York since Andy Roddick in 2001.
“I played a solid match with not many mistakes,” said Nadal, the reigning French Open champion.
“He’s a player who can play amazing shots but sometimes he can be very unpredictable with errors so I just waited for my opportunity.”
Nadal, the 2010 and 2013 champion in New York, showed no signs of the struggles that bedeviled him in the two previous rounds, when he dropped the opening set before prevailing in four.
His 23 winners on Monday were just shaded by world number 64 Dolgopolov’s 25 but the Ukrainian’s 39 unforced errors were more than three times those committed by Nadal.
Rublev, ranked 53, has won 13 of his last 17 matches after breaking the top 100 for the first time in June.
He marked his entry into the top 50 by winning the Umag title as a lucky loser in July.
“Rafa is a real champion. I will try to do my best — I have nothing to lose,” said Rublev, whose push to victory on Monday was helped by Goffin suffering a left knee injury.
“It was impossible to win today,” said the Belgian.
Federer, bidding for a sixth US Open and 20th major, will tackle Philipp Kohlschreiber later Monday.
After stretching his runs of dominance over Mikhail Youzhny to 17-0 and Feliciano Lopez to 13-0, the 36-year-old Federer takes an 11-0 advantage into his night-time duel with German 33rd seed Kohlschreiber.
The remaining last-16 tie of the day sees 2009 champion Juan Martin del Potro, the 24th seeded Argentine, up against Austrian sixth seed Dominic Thiem.
Thiem, who was forced to quit with injury against del Potro at the same stage in 2016, celebrated his 24th birthday on Sunday.
– One of Pliskova’s best –
Top seed Kristina Pliskova, the runner-up in 2016, needed just 46 minutes to sweep past Jennifer Brady of the United States 6-1, 6-0 and make her third Slam quarter-final of 2017.
The tall Czech had needed back-to-back three-setters to get to the last 16, including having to save a match point against Zhang Shuai of China in the third round.
But the 25-year-old world number one fired 23 winners on Sunday while the outclassed Brady, the 91st-ranked player, managed just six in her quickfire demolition.
Pliskova will next face either 37th-ranked compatriot Lucie Safarova or US 20th seed CoCo Vandeweghe for a place in the semi-finals.
“I think it was one of my best matches this year,” said Pliskova.
“But the opponent was not the best. Definitely she can play better than she was playing today.”
Ukraine’s Elina Svitolina, the fourth seed who is in a three-way tussle with Pliskova as well as the already-eliminated Garbine Muguruza for the world top spot, faces Madison Keys, the 15th seeded American.
Svitolina is looking to reach the quarter-finals of a Slam for the second time this season having also made the last-eight at Roland Garros in June.
Keys is playing in the last 16 in New York for a third successive season.
The winner of that clash will face either Russia’s Daria Kasatkina or Estonian qualifier Kaia Kanepi, ranked 418.
Kanepi is a five-time Grand Slam quarter-finalist including making the last eight in New York in 2010. DM
"You can't wait for inspiration. You have to go after it with a club." ~ Jack London