Gauff and Pegula have now won two championships this year after their first was won in a triumphant title defence at Doha in February.
Her victory over No. 7 Rybakina gave her 60 career victories in the Top 10, which puts her third among active players behind Venus Williams and Victoria Azarenka.
Since defeating Sinner in the Rotterdam final in February, Medvedev is now 6-0 against Sinner in their head to heads.
After losing their first two encounters, Rybakina finally defeated the American. With a 21-3 record, she is currently leading the tour in matches won in 2023.
The World No. 1 kept the American at arm's length in a smooth 6-4, 6-2 victory in a Thursday night quarterfinal.
Kvitova won the match after 2 hours and 12 minutes on a relatively dry afternoon to secure the final spot in the semifinal lineup.
Khachanov had to dig deep to register a fantastic 7-6 (7-4), 6-4 win over the Greek, who failed to get into his stride against the Russian.
Rybakina, who was also the champion at Indian Wells earlier this month, is well on her way to become the fifth woman to complete the sunshine double.
Fritz recorded eight aces and returned three out of four break points in the tie. His win percentages on the first and second serves were 56% and 62% respectively.
The Italian tennis player hit eight aces and returned three out of five break points, and his win percentages on the first and second serves were 85% and 68% respectively.