She outlasted Kasatkina in a 32-point rally for match point.
Swiatek, who improved to 2-0 in this year's competition following her own 6-3, 6-2 win over Caroline Garcia, goes through as the winner of her group, while Gauff can no longer qualify for the semifinals.
The win continues a phenomenal season for Swiatek, who rose to world No. 1 in April and has won eight titles, including two Grand Slams at Roland Garros and Flushing Meadows this year.
Kyrgios, Wimbledon finalist this year, has recorded the most wins on tour since the end of the French Open and continued the finest season of his career with a 7-6(11), 3-6, 6-3, 6-2 victory over Medvedev in a blockbuster fourth-round clash.
She lost 6-7(4) 6-2 6-1 in an all-American showdown in the third round.
The World No 1 had triumphed at Roland Garros in 2020.
World No. 1 Swiatek crushed her Russian opponent 6-2, 6-1 while teenager Gauff recorded a comfortable 6-3, 6-1 win over Trevisan in the semifinals.
She defeated Belgian Elise Mertens 6-4, 6-0 in the fourth round.
Gauff, who shot to fame as a 15-year-old when she reached the fourth round at Wimbledon in 2019, urged the 18-year-old Raducanu to take time away from her phone.
The pair appeared evenly matched early on but the 17-year-old Gauff handed Stephens a critical break with a double fault on the last point in the ninth game and never regained the momentum from her 28-year-old opponent.