That would put him just one behind Federer’s record mark and three clear of Novak Djokovic, both of whom are out after struggling with injuries in New York.
The 33-year-old Nadal will play 24th-seeded Italian Matteo Berrettini, who beat Gael Monfils in five sets, in the semifinal with a potential fourth US Open title on the line.
The other three men’s semifinalists — Berrettini, Grigor Dimitrov and Daniil Medvedev — have never played in a grand slam final.
“Today I make a step forward, in my opinion,” said Nadal in his on-court interview at Flushing Meadows.
“That match gives me confidence. Two matches in a row against two tough opponents.
“That’s a moment to increase a little bit more the level, and I really believe that I can do it.”
The quarterfinal was far from a walk in the park for Nadal, who won a record-extending 12th French Open this year, as Schwartzman twice recovered from four-game deficits.
But in an Arthur Ashe stadium full to the brim with vociferous Argentine supporters, Nadal hit 35 winners and broke serve eight times to quieten the crowd and overcome the combative Schwartzman in just under three hours.
He also had to call the trainer for a problem with his left forearm early in the final set.
“I had some mistakes of course but I am super happy the way I accepted the challenge,” said Nadal.
“I just keep going point by point and here I am in the semifinals and that is super important for me. It means everything.”
Schwartzman is a regular at Rafael Nadal’s Tennis Academy in Mallorca, and although he put up a tough fight, the familiarity gleaned from training at Nadal’s facility didn’t help him in stopping the number two seed.
Nadal has now reached the semifinals of all four majors in the same year for the second time in his career.
While Nadal was one of the favorites to win the US Open ahead of the competition, following Djokovic’s retirement through injury and Federer’s shock quarterfinal exit, he is now cemented as the front runner to lift the trophy.
Despite all three members of the “Big Three” being in their thirties, they have shown no evidence of slowing down — the past 11 Grand Slams have all been won by either Nadal, Djokovic or Federer.