Sakkari battled past world No. 3 Pegula 7-6(6) 7-6(4) to record her first win over a top-five opponent this year.
'I struggled to win my first WTA title. It took me time. So I believe this will take me time,' said the Tunisian.
It was twice French Open champion Swiatek's first major title on a hard court and the 21-year-old is the first Polish woman to win the US Open.
After a sluggish start, the Pole came alive in the second set and overcame an early break in the decider by winning the final four games to see off the powerful Belarusian.
Ons Jabeur executed a stunning 6-1 6-3 demolition of Caroline Garcia in the U.S. Open semi-finals on Thursday, ending the Frenchwoman's hot streak to reach her second Grand Slam final in a row.
Rybakina, the first Kazakh to enter a Grand Slam final, upset Simona Halep in the second semifinal.
Tunisian Jabeur, ranked third in the world in singles, has injured her right knee, Britain's Lawn Tennis Association said in a social media post.
Austrian Thiem, who has failed to win a match at any of the tournaments he has played since his wrist injury comeback in March, made 42 unforced errors as his once dominant claycourt game deserted him.
Jabeur defeated Estonian Anett Kontaveit 7-5, 6-3 in their Indian Wells quarterfinal.
Unseeded Collins ended Tunisian Ons Jabeur's dream run to set up a clash with Australian Open champion Sofia Kenin.