Meanwhile, world number one Novak Djokovic defeated Britain’s Kyle Edmund with 7-6(7) 6-1 to reach the Paris Masters quarter finals.
Naomi Osaka has withdrawn from the WTA Finals because of a right shoulder injury ahead of her scheduled round-robin match against top-ranked Ash Barty.
US Open runner-up Medvedev, chasing his fourth ATP Tour title in a breakthrough 2019 season, will meet Germany's Alexander Zverev in Sunday's final.
The three-time Grand Slam winner says he no longer has pain in his hip and it is now a matter of building up fitness so he can play several matches in a row at tournaments.
Williams will face Canadian Bianca Andreescu for the US Open title as the American sets herself up for another attempt to clinch a record-equaling 24th Grand Slam singles title.
Champion Novak Djokovic elected to retire in the third set due to a left shoulder injury. He was facing off Stan Wawrinka who was leading 6-4, 7-5, 2-1.
Serena Williams and Maria Sharapova will open the evening session at Arthur Ashe Stadium with their first-ever NY meeting in a match that may just have the feel of a championship final.
Eighth-seeded Khachanov rallied for a 6-7 (3/7), 7-6 (7/4) 6-2 victory over the volatile Australian, but the final set was close to farce, with Kyrgios engaged in a running dialogue with Irish chair umpire Fergus Murphy.
Simona Halep won the Wimbledon final after two sets (6:2, 6:2) against Serena Williams. It is her second Grand Slam victory and the first in Wimbledon.
Federer and Nadal each won their quarter-finals to set up an epic semi-final between the two, whilst world number 1 Djokovic will face Bautista Agut for a place in the final.
Seven-time champion Serena Williams wobbled several times before overcoming Alison Riske on her way to the semi-final.
Tsitsipas had never won a set in his previous three meetings against claycourt specialist and 11-times French Open champion Nadal, but the Greek drew first blood by saving a break point to hold in the 10th game and take the first set.
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