Pegula raced into a 5-1 lead against Sakkari on her way to taking the opening set and, on a wet and windy night, the 29-year-old was able to see out victory after winning the first four games in the second.
It is the first time Pegula has qualified for the semi-finals at the season-ending tournament, and she is the first American to reach the final four since Sloane Stephens in 2018.
"Getting through 3-0 is really kind of a cool accomplishment, especially coming off of last year, where it was the opposite," Pegula said.
Meanwhile, Belarusian top seed Sabalenka had taken charge of her crucial match against Rybakina, clinching the opening set with a double break.
But Kazakhstan's Rybakina will serve to force a third set when they resume on Friday after coming back from a break down to lead 5-3 in the second.
The players left the court at 23:40 local time - more than three hours after the match began - at the end of an evening interrupted by bad weather.
Sabalenka is set to retain her world number ranking if she reaches the final.
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