The 38-year-old Swiss, who is bidding for a record sixth title in New York, lost the first set before recovering to win 4-6 6-1 6-2 6-4.

Earlier on Monday, world number one Novak Djokovic progressed with a straight-sets victory over Spaniard Roberto Carballes Baena.

The Serb kicked off the defence of his title with a 6-4 6-1 6-4 win.

Djokovic, 32, has reached the final on his past three appearances in New York but was taken to four sets in his opening two rounds last year.

Djokovic, who has won 16 Grand Slams and is aiming to close the gap on Federer (20) and Rafael Nadal (18), faces Argentine Juan Ignacio Londero in the second round.

Federer also lost the first set in his opening match against South African debutant Lloyd Harris at Wimbledon last month, improving as the tournament wore on and eventually losing to Djokovic in the final.

Nagal, 22, has never won a tour-level match and was playing in the main draw of a Grand Slam for the first time, but tested his illustrious opponent before losing in two hours and 30 minutes.

Third seed Federer will meet Damir Dzumhur of Bosnia-Herzegovina in the next round at Flushing Meadows.

"I just tried to forget the first set, play tough and stay with him," said Federer, who last won the US Open in 2008.

"I wasn't serving consistently enough. I was hitting double faults that usually I don't do. Also I was just hitting too many unforced errors. I was in two minds, I guess.

"I was able to clear that a little bit. Maybe it's not a bad thing to go through a match like this."

Russian fifth seed Daniil Medvedev took just 85 minutes to see off Indian world number 88 Prajnesh Gunneswaran with a routine 6-4 6-1 6-2 win.

The 23-year-old, who has reached three consecutive tour finals this year, will face Bolivian world number 84 Hugo Dellien in round two.

"I can't say I'm feeling amazing about my game but to win by that score in the first round is great," he said. "I hope I can continue to play well."

Medvedev, who won the Cincinnati title earlier this month, is widely tipped as the man to put an end to Djokovic, Federer and Nadal's dominance.

"I always try to stay at the same time a little bit away [from such talk], because I always say at this moment of my career I haven't even been in the quarters of a Slam yet," he said.

"So that's the first step to make, and if I make this step, then I can talk about bigger goals and bigger achievements."

Japanese seventh seed Kei Nishikori raced into the second round when he took a 6-1 4-1 lead before Argentine opponent Marco Trungelliti retired with a back problem.

"It's a little bit sad to see. He's a great player," said Nishikori, who faces 108th-ranked American Bradley Klahn in the next round.

"I played great tennis from the beginning and I'm happy with the way I played. But honestly, I wanted to play a little more because I was feeling good on the court and I wanted to get a little more confidence."

Belgian 15th seed David Goffin overcame Frenchman Corentin Moutet 6-3 3-6 6-4 6-0 and will take on Cameron Norrie's conqueror, Gregoire Barrere, in round two.

Swiss 2016 champion Stan Wawrinka reached the second round with a 6-3 7-6 (7-4) 4-6 6-3 win over Italian Jannik Sinner. The 23rd seed will face Frenchman Jeremy Chardy next.

American 16-year-old Zach Svajda, who received a wildcard into the main draw, took Italian veteran Paolo Lorenzi, 37, to the wire in a thrilling 3-6 6-7 (5-7) 6-4 7-6 (7-4) 6-2 defeat.

World number 136 Lorenzi, called up as a lucky loser after former Wimbledon and US Open finalist Kevin Anderson pulled out with a knee injury on Saturday, takes on Serbian teenager Miomir Kecmanovic next.

But Italian 11th seed Fabio Fognini lost 6-3 6-4 6-7 (6-8) 6-3 to American 21-year-old Reilly Opelka, who will face German qualifier Dominik Koepfer in the next round.