Sixth seed Pegula repeatedly did what seemed nearly impossible to do lately against Swiatek, who counts the 2022 US Open among her five grand slam titles and has led the WTA rankings for most of the past two and a half years: break her serve.
The 30-year-old Pegula has won 14 of her past 15 matches and will now make her debut appearance in the semi-finals of a slam on Thursday (Friday AEST) against unseeded Karolina Muchova of the Czech Republic.
"Finally, I can say 'semi-finalist!'" Pegula told the crowd.
"I knew I could do it," she added.
Swiatek served poorly in the first set and her forehand was a real problem, with 22 of her 41 unforced errors coming on that side. Pegula used terrific defence to keep forcing Swiatek to hit an extra shot.
Iga Åšwiatek's frustration with her form was evident at times during the match. (AP PHOTO)
Entering Wednesday, Swiatek had lost just a pair of service games across four matches in the hard-court tournament, both in the first round - and she didn't even face a single break point in any of her most recent three contests.
But Pegula didn't have much trouble in that department, especially at the outset, breaking in each of Swiatek's initial two service games, which both ended with double-faults, and three of the first six.
It helped that Swiatek was unable to properly calibrate her first serves early, putting just 2 of 12 - 16.7 per cent - in play at the start, only 36 per cent for the opening set.
During Pegula's previous 0-6 rut in major quarter-finals, two of the exits came against Swiatek, and one was against another No.1 player, Ash Barty.
Muchova was the runner-up to Swiatek at the 2023 French Open and made it to the final four at Flushing Meadows for the second consecutive year with a 6-1 6-4 victory over No. 22 Beatriz Haddad Maia earlier in the day.
"It was me and myself, it was my ghosts inside my mind and I know all the tennis players have that," Haddad Maia said. "Today was like an inner fight. I couldn't manage that."
Karolina Muchova salutes the crowd after her quarter-final win. (AP PHOTO)
Muchova lost to champion Coco Gauff in the US Open semi-finals in 2023, but then needed surgery on her right wrist in October and was off the tour for about 10 months, returning this June.
That was the latest in a series of injuries for Muchova, who called it "one of the worst ones that I had."
"Now, looking back," she said, "I'm, like, 'Oh, it actually flew by, the time, and I feel strong again."
