The 23-year-old Pole was seeking her sixth Grand Slam title and her second title in New York.
Świątek entered the match as favorite and had looked in good form in the earlier rounds.
However, while Pegula has previously enjoyed little luck (three wins to six losses) against the Pole, she had been in a rich vein of form coming into the US Open, winning 13 of her last 14 matches, triumphing in Toronto and reaching the final in Cincinnati.
Pegula was again in fine form in the quarterfinals, breaking Świątek in the first game and again in the third to take a 3-0 lead inside 15 minutes.
For all Pegula’s good work, Świątek appeared to struggle with her open game, echoing her Olympic semifinal loss.
From the outset, the Pole racked up double faults, struggled with her first serve and registered nine unforced errors within the first two games.
Coach Tomasz Wiktorowski could be heard shouting from the stands in the opening set, encouraging Świątek to “play your forehand to her backhand.” His words failed to reverse the tide. Świątek’s 19 unforced errors to Pegula’s 12 opened the door for the American to dominate the opening set (6:2).
Świątek’s typical locker room break after the first set seemed to help her refocus, and she began the second set in a more positive fashion, finding more consistency with her first serve in the first game, going 1:0 up.
But Pegula maintained her composure and looked calm and confident on the court. She handled her service game brilliantly, and after numerous unforced errors from the Pole, she broke serve to make it 2:1.
Świątek bounced back in the fourth game, notching up her first break to make it 2:2, stepping up a gear and holding her serve for 3:2.
Pegula, however, remained unfazed and won the next three games to take a 5:3 lead. Both players found their rhythm and the overall quality of the match improved to feature longer and more spectacular rallies.
But it was Pegula, serving brilliantly, who took a 40/0 lead at 5:4. After squandering the first two match points, Pegula made it third-time lucky to advance into her first ever Grand Slam semifinal.
Świątek will remain world No. 1 regardless of results elsewhere in New York largely thanks to her strong displays earlier on in the season.
After finishing this match with 41 unforced errors to her opponent’s 22, Świątek appeared to face similar issues to those that impacted her Olympic semifinal against Zheng; if she is to be toppled off top spot, it will likely owe more to her own loss of consistency than her rivals' dramatic improvements.
Pegula will now play Czech Karolína Muchová while Belarusian Aryna Sabalenka will face American Emma Navarro in the other semifinal.
