Jessica Pegula is back in the quarterfinals at the U.S. Open after a 6-4, 6-2 victory over Diana Shnaider on Monday, her seventh trip to that round at a Grand Slam tournament. Now comes the hard part: Pegula is 0-6 in major quarterfinals over her career — and this next one will come against No. 1 Iga Swiatek.

The No. 6-seeded Pegula, an American whose parents own the NFL's Buffalo Bills and NHL's Buffalo Sabres, is on quite a run at the moment, having won 13 of her past 14 matches, all on hard courts. That included her second consecutive title in Canada and an appearance in the final at the Cincinnati Open, where she lost to No. 2 Aryna Sabalenka.

"I feel like there's been more pressure this year, because I did so well coming into this tournament," said the 30-year-old Pegula, the oldest woman left in the field. "I want to keep working my way and hopefully bringing my best tennis for the later rounds this time."

Swiatek was tied at 4-all with No. 16 Liudmila Samsonova on Monday night before grabbing seven straight games en route to winning 6-4, 6-1. When Swiatek captured the 2022 U.S. Open for one of her five Grand Slam titles, she eliminated Pegula in the quarterfinals.

"She's in a good rhythm right now, and she won so many matches past weeks," Swiatek said about Pegula, "that, for sure, it's going to be a challenge."

Indeed, half of Pegula's six quarterfinal exits at Slams came against a No. 1 player — Swiatek twice and Ash Barty once.

"I'll just try to draw from those experiences and kind of how I felt going into the next match, but it's just so tough," Pegula said. "I mean, I know you don't want the cliche answer, but it's just kind of one match at a time, and every day kind of feels different. It depends on who you are playing, how the conditions are, when you're playing. There are so many variables day to day."

Also returning to the quarterfinals was Karolina Muchova, a 6-3, 6-3 winner over No. 5 Jasmine Paolini, the runner-up at the French Open and Wimbledon this season. Muchova next plays No. 22 Beatriz Haddad Maia, who got past 2018 Australian Open champion Caroline Wozniacki 6-2, 3-6, 6-3 to become the first woman from Brazil in the U.S. Open quarterfinals since Maria Bueno in 1968.

Haddad Maia is a 28-year-old left-hander who was given a 10-month suspension after failing a doping test in 2019. She was a semifinalist at the French Open last year but had not been past the second round at Flushing Meadows until now.

Muchova enjoyed a breakthrough 2023, getting to the final in Paris and the semifinals in New York, before needing surgery on her right wrist in October, sidelining her for 10 months.

"This was my worst and most serious injury, I would say. But, I mean, I love the sport, so in my head, I was like, 'I will do everything I could to [get] better and try.' And here I am today," said Muchova, whose U.S. Open ended a year ago with a loss to eventual champion Coco Gauff. "I'm just a really happy kid now."

Gauff was seeded No. 3 this year and was eliminated Sunday by No. 13 Emma Navarro.

In men's action Monday, No. 1 Jannik Sinner beat No. 14 Tommy Paul 7-6 (3), 7-6 (5), 6-1 at night to set up a quarterfinal showdown against 2021 champion Daniil Medvedev.

No. 5 Medvedev, the only past men's winner still in the bracket, overwhelmed beat Nuno Borges 6-0, 6-1, 6-3 in a victory delayed for six minutes — along with every other match going on at the time — because of a fire alarm in the building that houses the electronic line-calling system.

No. 25 Jack Draper became the first British man to reach the quarterfinals in New York since the recently retired Andy Murray did it in 2016. Draper, who exited in the fourth round a year ago, will appear in his first Slam quarterfinal thanks to a 6-3, 6-1, 6-2 win against unseeded Tomas Machac.

"I obviously miss Andy. Shoutout to Andy. What an unbelievable career the guy's had. Just an icon of the game. I miss him in the change rooms. I miss being next to his stinky shoes and all his stinky clothes," said Draper, who'll take on No. 10 Alex de Minaur, a 6-0, 3-6, 6-3, 7-5 winner against Jordan Thompson in an all-Australian matchup. "Andy's a legend, and if I have half the career he had, then I'll be a happy man."

Everything went Pegula's way against the 18th-seeded Shnaider, a 20-year-old Russian who played one season of college tennis at NC State and won a silver medal in women's doubles at the Paris Olympics.

Pegula compiled 22 winners, hit six aces, saved 7 of 9 break points that she faced and claimed five of Shnaider's service games.

"My movement has really improved, which has really helped me stay into a lot of these points and these sets and these games and be super consistent," Pegula said. "I've been serving pretty well. Even if it's not working, I've been kind of getting myself out of service games by serving smart or serving well in big moments like today where she was returning really well."