The Russian will face either Dusan Lajovic of Serbia or American Frances Tiafoe for a place in the quarterfinals of the prestigious ATP Masters and WTA hardcourt tournament.
In her first match since winning the Australian Open, women's world number two Naomi Osaka beat Ajla Tomljanovic 7-6 (7/3), 6-4.
Serbian tennis player Novak Djokovic breaks Roger Federer's record for most weeks as the men's top number one, and plans to win many more Grand Slams.
Russian Medvedev, who has won nine matches in a row, beats Spanish Nadal, world number two, 3-6, 7-6 (7/4), 6-3 during their ATP semi final match.
Austria's Dominic Thiem steamed into his first US Open final after defeating Russia's Daniil Medvedev 6-2, 7-6 (7), 7-6 (5).
Djokovic's win gave Serbia an unassailable 2-0 lead ahead of the doubles to set up a meeting with either the Nick Kyrgios-led Australia or Rafael Nadal's Davis Cup champions Spain in the final.
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 33-year-old Spanish left-hander moved one shy of Roger Federer's all-time men's record 20 Grand Slam triumphs and became the second-oldest New York champion in the Open era after Ken Rosewall in 1970 at age 35.
Spain's Rafael Nadal will play for his 19th Grand Slam title, one shy of Roger Federer's all-time men's record, against No. 5 seed Daniil Medvedev of Russia on Sunday.
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.
An erratic Novak Djokovic suffered a surprise 6-3, 4-6, 6-2 defeat against the 10th-seeded Russian Daniil Medvedev in the Monte Carlo Masters quarter-finals.
Roger Federer was challenged by Fernando Verdasco before defeating the Spanish veteran 6-3 3-6 6-3, reaching the quarter-finals of the Dubai Duty Free Tennis Championships.
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