The sixth seed threw her hands into the air after closing out the biggest win of her career in front of the elated home crowd at Arthur Ashe Stadium in her seventh major quarter-final.
"I've been (to the quarters) so many freaking times - I just kept losing," she said. "Finally I can say semi-finalist."
Swiatek, who withdrew from last month's Canadian Open citing fatigue, appeared out of sorts from the start as she struggled with her serve and helped her opponent with 41 unforced errors.
The Pole had not been broken since the first round of the tournament but dropped serve with a double fault in the opening game and again in the third.
Pegula looked in cruise control in the second set as she broke Swiatek again in the third game but the 2022 champion showed signs of life as she broke back with a forehand winner in the fourth.
Pegula would not let her opponent take the momentum, however, keeping up the pressure from the baseline in a four-deuce game seven, as Swiatek smacked her thigh with frustration after sending a forehand out on break point.
Pegula led 40-0 in the final game but needed the encouragement of the home crowd to get her over the line as Swiatek produced a pair of fine winners to stay in it.
The American was finally able to celebrate when Swiatek sent a shot out on match point.
"Thank you to the crowd," she said. "You carried me through the last game."
Pegula joins compatriot Emma Navarro in the final four and will next play Czech Karolina Muchova.
Americans Taylor Fritz and Frances Tiafoe have also reached the semi-finals in the men's draw.
