Novak Djokovic ensured he will return to the top of tennis's world rankings with an emphatic first round victory at the US Open on Monday as women's world number one Iga Swiatek and American rival Coco Gauff advanced.

Djokovic, chasing a record-extending 24th Grand Slam singles title in New York, shrugged off a late-night start on the Arthur Ashe Stadium to demolish France's Alexandre Muller 6-0, 6-2, 6-3 in just 1hr 35min.

The win means Djokovic is guaranteed to replace defending US Open champion Carlos Alcaraz as world number one when the tennis rankings are next updated after the tournament.

Djokovic is playing in New York for the first time since suffering an agonising defeat in the 2021 final in New York.

He was barred from entry to the United States in 2022 for his refusal to get vaccinated against Covid-19, meaning he was unable to play the US Open.

On Monday the 36-year-old played like a man making up for lost time, reeling off 32 winners and breaking Muller eight times in a lopsided encounter that finished at around 12.40am local time.

Djokovic, who will face Spain's Bernabe Zapata Miralles in the second round, said he was unfazed by the late start to his game.

"I didn't care if I started after midnight because I was looking forward to this moment for few years, to be out on the biggest stadium in our sport, the loudest stadium in our sport, playing night session," Djokovic said. "It was a great joy to be stepping out on the court.

- 'Flawless' tennis -

"I think the performance explains how I felt tonight, particularly in the first two sets. It was kind of lights-out tennis really, almost flawless, perfect first set.

"Overall I'm very, very pleased with the way I feel, with the way I'm playing. Hopefully I can maintain that level."

Djokovic's arrival on court had been delayed after a gruelling three-set battle between American teenager Gauff and Germany's Laura Siegemund in the preceding night game.

The 19-year-old Gauff, tipped by many as the biggest threat to defending US Open champion Swiatek, was forced to dig deep before winning 3-6, 6-2, 6-4 in 2hr 50min.

An ill-tempered clash was marked by tetchy confrontations by both players with chair umpire Marijana Veljovic.

Gauff accused the Serbian official of failing to properly enforce time violation rules against Siegemund.

"I felt like the rules were being bent," Gauff said. "That's why a lot of players get mad when these time violations are called because one ref is letting them go over, the other is more strict on the time."

Siegemund, 35, meanwhile voiced disgust at the partisan New York crowd, describing them as "respectless" for the way they cheered every error or missed first serve.

"They had no respect for me, no respect for the way I played, no respect for the player that I am, they had no respect for good tennis," Siegemund said.

- Swiatek powers through -

In other women's games on Monday, defending champion Swiatek needed less than hour to defeat Sweden's Rebecca Peterson 6-0, 6-1.

The 22-year-old world number one from Poland overwhelmed her opponent with five breaks of serve and 20 winners to complete victory in just 58 minutes on the Arthur Ashe Stadium.

"I wanted to start the tournament with everything I was focusing on. I was happy to play a great game, with all the pressure and expectations I was happy on the court," said Swiatek after her win.

Swiatek, targeting her fifth Grand Slam title, will face Daria Saville of Australia in round two.

While Swiatek advanced safely, there was no such luck for Greece's eighth seed Maria Sakkari, who became the highest ranked early casualty, beaten 6-4, 6-4 by Spain's Rebeka Masarova, ranked 71st in the world.

Kazakhstan's fourth seed Elena Rybakina was an easy winner over Ukraine's Marta Kostyuk, cruising through to the second round with a 6-2, 6-1 victory.

There was also a win for former world number one Caroline Wozniacki, making her first Grand Slam appearance in over three years.

The 33-year-old Danish mother-of-two, who came out of retirement earlier this month, defeated Russian qualifier Tatiana Prozorova 6-3, 6-2.

Back in the men's draw meanwhile, Djokovic's route to a potential final meeting with Alcaraz was made easier as Danish fourth seed Holger Rune was stunned in four sets by Spanish journeyman Roberto Carballes Baena, a clay-court specialist ranked 63rd in the world.

Carballes Baena punished an error-strewn display by Rune to win 6-3, 4-6, 6-3, 6-2.

Last year's US Open runner-up, Norway's fifth seed Casper Ruud, reached the second round with a battling 7-6 (7/5), 3-6, 6-4, 7-6 (7/5) defeat of Emilio Nava of the United States.