The 23-year-old was returning to action just a week after it was revealed he had failed two drug tests in March.

However, he escaped a lengthy ban from the sport when officials decided he wasn’t at fault for the presence of banned anabolic agent clostebol in his system.

“I was a little bit not in the best way,” said Sinner of his victory.

“The first match is not easy. He played really well in the beginning so I just tried to stay there mentally and find some rhythm to keep going.”

French Open champion Swiatek, chasing a second New York title to add to her four triumphs in Paris, saw off Russian lucky loser Rakhimova 6-4, 7-6 (8/6) to extend her season-leading record to 54 match wins.

However, it was an unconvincing display by the Pole who committed 41 unforced errors and had to fight off three set points in the second set.

“I try to adapt to the court and feel how it is,” said Swiatek.

“I’ll take it day by day to get more rhythm. It’s the biggest stadium we have and you feel it’s a huge deal.”

Osaka, who missed last year’s tournament after giving birth to her daughter Shai, stunned 10th seed Jelena Ostapenko.

Former world number one Osaka, now ranked 88, came through 6-3, 6-2 for her first top 10 win in four years.

The Japanese star crunched nine aces in her 19 winners and committed just five unforced errors to her opponent’s 21.

Her tennis was as striking as her outfit. Osaka arrived in court with a brightly-coloured, giant bow on the back of her jacket and a frilly skirt over her playing dress.

To complete the ensemble, the 26-year-old attached small bows to the heels of both shoes.

“Last year I was watching Coco (Gauff) play and I so badly wanted to step on these courts again,” said a tearful Osaka, a four-time major winner.

‘Means so much’

“I didn’t know if I could … just to win this match and just to be in this atmosphere means so much to me.”

Osaka’s fellow tennis mum Caroline Wozniacki, runner-up to Serena Williams 10 years ago, needed just 53 minutes to see off Japan’s Nao Hibino 6-0, 6-1.

Daniil Medvedev, the Russian fifth seed who shattered Novak Djokovic’s dream of a rare calendar Grand Slam by claiming the 2021 US Open, went through with a four-set victory over Dujan Lajovic of Serbia.

Carlos Alcaraz, who won the first of his four Grand Slam titles in New York in 2022, opens the night session on Arthur Ashe Stadium against Australian qualifier Li Tu, the world number 186.

Alcaraz is on a 14-match winning streak in Grand Slam events and is attempting to become the only third man in the modern era to win the French Open, Wimbledon and US Open in the same year after Rod Laver in 1969 and compatriot Rafael Nadal in 2010.

Li, 28, hasn’t won a match on the main tour in 2024.

Elsewhere on Tuesday, 2021 semi-finalist Felix Auger-Aliassime, the 19th seed, slipped to a straight-sets loss to Jakub Mensík of the Czech Republic.

Tsitsipas out

Greek 11th seed Stefanos Tsitsipas, who has never made the second week at the US Open, was stunned 7-6 (7/5), 4-6, 6-3, 7-5 by Australia’s Thanasi Kokkinakis.

Fourth seed Elena Rybakina, the 2023 Wimbledon champion, enjoyed a 6-1, 7-6 (7/1) win over 194th-ranked Australian qualifier Destanee Aiava.

Stan Wawrinka, the 2016 winner, aims to become the third man in last 50 years to win a main draw match at the tournament at the age of 39 or over after a 40-year-old Jimmy Connors in 1992 and Ken Rosewall — who was 42 when he achieved the feat.