“The beginning, the first match, is always a little bit new even if I’ve played here plenty of times,” said Nadal, who meets Aussie Thanasi Kokkinakis next. “I think I played well and in general am very happy with the way I started.
“He (Millman) showed last year what he’s able to do when he’s doing well and I came on court with a lot of respect.”
Two-time French Open runner-up Thiem was upset by Italian giant-killer Thomas Fabbiano 6-4, 3-6, 6-3, 6-2, as the Austrian slumped to another first-round exit, having lost at the same stage at Wimbledon.
“I got very tired and exhausted after two sets. I’m far away from 100 percent,” Thiem said. “It was not the real me there on the court.”
Greek eighth seed Tsitsipas struggled with cramps and accused umpires of having “preferences” after he fell to a 6-4, 6-7 (5/7), 7-6 (9/7), 7-5 defeat by Next Gen rival Andrey Rublev in a gruelling four-hour slog.
Tsitsipas, for whom it was also a second successive Grand Slam opening-round defeat, was hit with a point penalty for a time violation in the final set.
“This chair umpire, I don’t know, he has something against me. I don’t know why,” said Tsitsipas, who snapped “you’re all weirdos” at French official Damien Dumusois during his match.
“I wish that all the chair umpires were like Mohamed Lahyani because I believe he’s the best out in the game, and we need more like him in tennis because he’s fair to everyone. I feel like some of them have preferences when they are on the court.”
Osaka struck by nerves
Russian ninth seed Khachanov lost to Canada’s Vasek Pospisil in five sets, with 10th seed Bautista Agut of Spain succumbing in similar fashion to Mikhail Kukushkin of Kazakhstan to leave that quarter of the draw, which features Nick Kyrgios, wide open.
Alexander Zverev, seeded sixth, battled into the second round by defeating Moldova’s Radu Albot 6-1, 6-3, 3-6, 4-6, 6-2, while Marin Cilic, the 2014 champion, advanced in straight sets over Slovakia’s Martin Klizan.
Reigning women’s US Open champion Naomi Osaka confronted severe nerves to come through in three tough sets against Russia’s Anna Blinkova, the world number 84.
Osaka suffered a first-round exit last month at Wimbledon and the Japanese star struggled to put away Blinkova before prevailing 6-4, 6-7 (5/7), 6-2.
“I have a lot of really good memories here because I grew up in this area. I don’t think I’ve ever been this nervous in my life,” said Osaka, sporting a black brace on the left knee that prompted her to retire in Cincinnati.
“You want to do well after you did well last year. I definitely didn’t want to lose in the third set.”
The top seed goes on to face Poland’s Magda Linette.
Osaka must retain her US Open crown to have a chance of remaining world number one and was tested extensively by 2015 Wimbledon junior finalist Blinkova, who raced 4-1 ahead in the first set and saved a match point in the second to force a decider.
Wimbledon champion Simona Halep, ousted in the opening round the past two years at Flushing Meadows, outlasted US lucky loser Nicole Gibbs 6-3, 3-6, 6-2.
“I feel much better that I could win a match finally in this tournament,” Halep said. “I’m not feeling great at the beginning of the tournament. But always when I played tough matches at the beginning, then I went through the semi-finals or quarter-finals. So I’m confident. I feel like my game, it’s there.”
Fifteen-year-old Wimbledon sensation Coco Gauff edged past Anastasia Potapova, 18, in three sets on her US Open debut.
