The top-seeded woman had even less trouble than Nadal did: 2016 runner-up Karolina Pliskova beat 91st-ranked American Jennifer Brady 6-1, 6-0.
But del Potro won their meeting in the 2009 final in NY in five sets for his only Grand Slam title, ending Federer's streak of five straight U.S. Open championships - and he hasn't won the trophy since. American CoCo Vandeweghe, beat Lucie Safarova 6-4, 7-6 (2).
Also in the quarters is Kaia Kanepi of Estonia, who became the second qualifier in the tournament's history to reach the quarterfinals and the first to do so since 1981.
"Rafa is the real champion and I am going to just try and enjoy it", Rublev said afterwards, who is looking ahead to facing one of his childhood idols.
"Let's make it four from four", said Vandeweghe.
After Federer won the second set, he took a medical time out and went into the trainer's room.
Rublev was shaky from the first game and double faulted twice en route to gifting Nadal - who had won his 50th US Open match in the previous round - a first break.
But, the flashes of the old Del Potro have resurfaced in NY in his run to the quarter-finals and a date with Federer today.
Nadal, 31, saw off Argentine lucky loser Leonardo Mayer 6-7 (3/7), 6-3, 6-1, 6-4, taking his record over the world number 59 from Buenos Aires to 4-0.
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Result: the price of frozen orange juice traded on the platform, the Inter Continental Exchange in NY jumped. India's Sensex advanced 0.3 percent to 31,807.05 and benchmarks in Taiwan and Southeast Asia also gained.
Rafael Nadal entered the U.S. Open as the new number one, but off of inconsistent performances at the Montreal and Cincinnati Masters events.
Now Nadal gets to play a fifth consecutive unseeded foe in Rublev, who took out No. 9 David Goffin 7-5, 7-6 (5), 6-3.
It will be a rematch of the 2009 U.S. Open final, when del Potro won his only Grand Slam title.
It will be Nadal's 26th semi-final in a slam, his sixth in NY. If he gets past him, the next challenge is expected to bring in a certain level of excitement as he will face the victor of Thiem vs. del Potro collision. Federer did not lose any of the sets he played in seven matches at the All England Club.
An ailing Juan Martin Del Potro came back from the brink of defeat to beat Austrian sixth seed Dominic Thiem 1-6 2-6 6-1 7-6 (1) 6-4 and reach the last eight of the US Open on Monday.
He has undergone four wrist surgeries, missed 10 Grand Slams and, at one stage a year ago, his world ranking slumped to 1,045.
At one stage past year, his world ranking slumped to 1,045 and he even considered retiring.
Having been well below his best in five-set wins over Frances Tiafoe and Mikhail Youzhny in the first two rounds, Federer appeared to have shrugged off concerns over his form and fitness by easing past Feliciano Lopez and then Philipp Kohlschreiber on Monday.
Back in 2008, legendary boxing promoter Don King, never short of hyperbole, even dubbed the potential clash as "Grapple in the Apple". No longer a "pattern server", where players in the past could easily guess the location of his first and second offerings, Nadal is now hitting the balls to all corners of the service box on both first and second serves and with increased velocity.