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It may not be immediately obvious from the minimal fanfare she generates compared with many of her compatriots, but Jessica Pegula is the highest ranked US tennis player, man or woman, and throughout this summer she has continued to back it up.

On Arthur Ashe Stadium against an in-form multiple grand slam champion, Pegula, the No 8 seed, took another significant step forward in her career by routinely dismantling Petra Kvitova 6-3, 6-2 to reach the US Open quarter-finals for the first time.

“It feels amazing. I’m so happy,” she said. “I knew Petra would be really tough, just the way she can hit winners from anywhere in the court. I thought I handled my nerves really well and that was the first time I have beaten her as well and that’s always nice.”

In a career-best season defined by her consistency, clean ball-striking off both wings and the high base level she has produced throughout the year, Pegula has now reached the quarter-finals of three grand slam tournaments this year, after also doing so at the Australian Open and the French Open.

As Kvitova burned hot and cold, struggling to control her unforced error count, Pegula dismantled her opponent with her brand of calm, controlled aggression. After conceding a tight first set, Kvitova started the second set well, breaking for a 2-0 lead. Pegula responded by winning six games in a row to set up a quarter-final meeting with Iga Swiatek.

After spending most of her career outside the top 100, the improvements to Pegula’s game have been exponential and she has been extremely consistent throughout the season at big events, even though she has won only one title.

She discussed her lower profile just before the US Open in Cincinnati, explaining why she believes her story is not as easy to root for. Pegula is the daughter of the billionaire businessman Terry Pegula, who is the owner of the Buffalo Bills NFL team.

“With my family and stuff, I know I was more privileged than other people, and I’m aware of that,” she said. “I try to be very down-to-earth, and I think I am. I know that’s maybe not the story people gravitate towards, right? They may think it’s interesting. I know some people do, but I’m aware of that and I know that.”

Pegula will face Swiatek in the quarter-finals after the world No 1 fought back from losing the first set to beat Germany’s Jule Neimeier 2-6, 6-4, 6-0. Swiatek was not at her best but rallied from a break down in the second set to advance.

“I’m just proud that I didn’t lose hope because she was playing really good in the first set,” Swiatek said after seeing off her highly-rated opponent, who reached the quarter-finals at Wimbledon. “I’m pretty glad that I used my experience to keep the same kind of level throughout the whole match.”