Two-time champion Naomi Osaka overcame a flurry of ‌mistakes to fight past Katerina Siniakova of the Czech Republic, finding her mettle to reach the third round of the US Open.

The 13th-seed has spent years taming her own tendency toward self-recrimination and showed the best evidence of her new career outlook ​as she reclaimed her composure with a bathroom break before the third set at Arthur Ashe Stadium.

“I think I was a little bit too hard on myself, so I took the bathroom break, tried to regroup and have no regrets,” said Osaka, who will ​play Belgian Elise Mertens.

The winner in 2018 and 2020 was pristine through the first set, with just four unforced errors, as she broke ⁠her opponent to love in the fourth game. The Czech did herself no favours with three ‌double ‌faults ​in the eighth game before letting Osaka break again on set point with an unforced error.

It was a different story in the second set, where Osaka’s form dropped ⁠just as Siniakova hit her stride, and ​the Japanese 13th seed put up 20 unforced errors ​that gave the Czech too many chances.

After trading breaks twice in the second set, Osaka tapped her racket on ‌the court in frustration after whacking a backhand ​into the net and handed Siniakova the break with another backhand error in the penultimate game.

Osaka went ⁠to the locker room before the third set, ⁠a decision that helped ​her move on.

“Obviously the match was really difficult. I think on my end it was more, like, mentally I wanted to play perfectly. Obviously that’s not going to happen every day,” said Osaka.

“In the third set, I just tried to do what I could do, and thankfully I was able to win.”

She emerged back on the court with new resolve, sprinting through the first three games and saving two break points in the fifth before closing it out with an unreturnable serve.

Osaka ‌has provided some of Flushing ⁠Meadows’ most memorable moments – from her breakthrough win in 2018 to her public advocacy for racial justice on her way to the title in 2020 – and said she was able to pull from her “memory ‌bank” of compelling wins to help her power through.

“When it gets to the third set, I try to think of all of ​the matches I was able to pull through,” said Osaka, who reached ​the semi-finals a year ago.

“I was trying to tell myself in the third set, like, keep going and keep trying to take the opportunities.”

Meanwhile in the Grandstand, Iga Świątek swept aside unseeded Argentinian Nadia Podoroska in straight sets to march on to the third round where she will meet 25th-seed Marie Bouzkova.

In the men’s singles, Taylor Fritz delivered another ‌commanding performance to beat Mattia Bellucci, extending his emphatic start to the tournament ​without dropping a set.

Fritz is among a handful of contenders looking to end a 23-year American wait for a men’s Grand Slam singles champion after Andy Roddick’s 2003 triumph at Flushing ​Meadows.

“I came out feeling really good, I felt confident with the ‌way ‌I ​was playing,” Fritz said after his ​98-minute demolition job.

“In the whole match, there wasn’t much nerves. I was aggressive and it felt great.

“It’s fun, playing a ​match like that on Arthur Ashe Stadium. I don’t know if there’s ‌many more things better than ​that, it’s a great feeling.”

The 2024 runner-up gave his unseeded ⁠Italian opponent no chance to ⁠settle as ​he dictated terms from the baseline and raced through the opening set in 35 minutes without conceding a game.

A timely ace in a tight game helped Bellucci open his account in the next set, but it was all Fritz from there as the 28-year-old ‌home favourite reeled off ⁠games to double his lead in the match.

Bellucci was unable to upset the pattern in the ‌third set as Fritz remained in control, sealing another easy win to set up ​a meeting with 24th-seed Francisco Cerundolo, ​keeping his bid for a maiden Grand Slam title on track.