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Alcaraz became the first man to defend a championship in the California desert since Novak Djokovic won three straight between 2014 and 2016.
Sakkari got the better of US Open champion Coco Gauff in a hard-fought second semifinal.
She had also missed the season-ending championships in Cancun due to the injury.
Pegula, who came into the contest with a dismal 1-4 record against the hard-hitting Sabalenka, managed to absorb her powerful serve to extend rallies and thwart the Belarusian's comeback attempts.
Pegula won 10 of the last 12 games to get past an error-prone Rybakina and notch up a 7-5, 6-2 win.
Protests by Just Stop Oil campaigners interrupted play twice during matches on Court 18.
World No. 106 Shnaider made a habit of roaring in Sakkari's direction and throwing her icy stares, and it got too much for the Greek sixth seed at 5-5 in the second set at Margaret Court Arena.
Sakkari is the first player from her group through to the last four.
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.
It was Pegula's 41st match victory in WTA main draws this year, with only world No. 1 Iga Swiatek (62) and the second-ranked Ons Jabeur (46) winning more.
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