Novak Djokovic strolled into the third round of the US Open, completing a 6-4, 6-1, 6-1 victory against Bernabé Zapata Miralles of Spain. As the second seed advanced, another of the few true potential threats in his half was removed. Stefanos Tsitsipas, the seventh seed, was beaten 7-5, 6‑7 (2), 6-7 (5), 7-6 (6), 6-3 by Dominic Stricker of Switzerland.

Tsitsipas’s exit is the second significant defeat in the bottom half after Holger Rune, the fourth seed, fell to Roberto Carballes Baena in the opening round. Afterwards, Tsitsipas denied his result had anything to do with the recent changes to his team. He is in New York with Mark Philippoussis as his head coach as his father remains at home.

As Djokovic continues to look imperious on the court, he will face his Serbian compatriot Laslo Djere for a spot in the fourth round. “Once you’re in the tournament, you need to be ready. Even if you think you’re not, you have to tell yourself you are and keep striving to improve,” Djokovic said.

Despite a positive opening win against Alexander Bublik, the 25th seed, Dominic Thiem’s miserable luck continued as he was forced to retire from his second‑round match against Ben Shelton with illness. Thiem, who also withdrew from Winston-Salem last week because of illness, called the doctor after losing the first set 7-6 (1).

Thiem explained he had vomited before the match and he continued to feel terrible. “I’m completely fucked,” he said of his physical condition. A number of players have been ill at the US Open so far, including Ons Jabeur, suggesting there may be a bug spreading inside the locker room.

Elsewhere Iga Swiatek, the top seed, reached the third round with a comfortable 6-3, 6-4 win against Daria Saville while Coco Gauff won the teenage battle on Arthur Ashe Stadium as the 19-year-old eased past the 16-year-old Mirra Andreeva 6-3, 6-2.

Lily Miyazaki’s dream run from the qualifying draw came to an end on Wednesday as Belinda Bencic, the 15th seed, reached the third round with a 6‑3, 6‑3 win.

The two first faced each other aged nine and seven respectively at a regional tournament in Switzerland, where Bencic was born and Miyazaki spent five years of her life. In the years since, their paths have sharply diverged.

The highest-ranked player Miyazaki had previously faced was the world No 48 Beatriz Haddad Maia, last year. Bencic, the Olympic gold medallist, demonstrated her superior quality in two tough sets

As they shook hands at the net, Bencic asked if Miyazaki remembered their childhood encounter, prompting both to laugh at their shared memory. Bencic went on to enjoy one of the most successful junior careers of recent times before transitioning seamlessly as a precocious teenager on to the tour where, now 26, she has remained. Miyazaki, meanwhile, moved to London with her family a year later. Her tennis journey took her to the University of Oklahoma on a scholarship, where she spent five years before finally starting her career. Her progress has been gradual.

After meeting again 18 years later at one of the biggest tournaments in the world, Bencic reflected on the different pathways to success. “You play some people in juniors – you would never think that they would become good and then they end up being better than you,” she said. “You can never say: ‘This girl is so good, so early, that’s why she’s going to be so good.’

“There are players like Ons [Jabeur], Maria Sakkari and they came later to the top. They were a little bit around 100, around 80 and just shaping their game. Now they’re top. Everyone has their own path, there’s no timeline for everyone. It doesn’t matter what age you are – you can play well at 18 and you can play well at 28.”

Miyazaki will rise approximately 45 places from her ranking of 198 and smash the career high of 169 she achieved in January. She will receive $123,000 (£96,700), a third of her career prize money before this week.

“I’ve learned that if I put my level out there then I have the game to really disrupt other players,” she said. “Because even today, once I got into the points I was able to play my game and control the points pretty well. I can take a lot of confidence from that.”