The world No.1 Jannik Sinner became the first player to equal Rafael Nadal's winning streak against Novak Djokovic from the 2013 season with his third successive win over the Serbian legend and his seventh overall in the 2024 season.
Medvedev has won a tour-best 58 matches this season, 43 in straight sets. He has yet to drop a set this week.
Federer saved five match points in the second set and received a point penalty in the third in the 6-3, 6-7 (7), 6-3 loss to fifth-seeded Alexander Zverev.
The second-seeded Federer, who is bidding to win a third Shanghai Masters title, dominated in the first set, but was tested in the second.
The Indo-Canadian pair notched up a 6-1, 6-4 win over Khachanov and Rublev in the opening round.
Serbia's Novak Djokovic climbed one spot up to the second, after claiming the Shanghai Masters title for the fourth time in a row on Sunday.
Djokovic holds an 11-0 overall record in finals played in China, where he also won the Beijing tournament six times and the 2008 year-end Tennis Masters Cup.
Coric earned passage to the final by taking down the top-seeded Federer 6-4, 6-4 in the semifinals on Saturday.
Federer, the defending champion, beat Daniil Medvedev 6-4, 4-6, 6-4 in the second round despite being broken late in the second set.
Djokovic's second-round victory improved his perfect record against the 41st-ranked Chardy to 12-0 in matches played, and 28-0 in sets won.
After his second title in Shanghai, the 36-year-old said that he has shaken off the "scars" of his many defeats to Nadal.
The Shanghai Masters is Federer's 94th career title, moving him into a tie with Ivan Lendl in second place on the Open era list.
Nadal holds a 23-14 winning record over Federer, but Federer has won their last four meetings, including all three this season. Nadal has won 14 of 23 finals against Federer.
It will now be the fourth time and third time in a final when Federer and Nadal will clash with each other this season.
The world number one Nadal, who won a tour-best sixth title of the season at the China Open last week, has now beaten Marin Cilic in five of their six matches.
Del Potro tumbled on the court at 2-2 in the third set against Viktor Troicki and instinctively tried to break the fall with his left wrist in the quarterfinal in Shanghai on Friday.
The Swiss tennis maestro dismantled Gasquet 7-5, 6-4 in a one-sided match that lasted more than an hour.
Topping Grigor Dimitrov of Bulgaria 6-4, 6-7 (6), 6-3 was his 870th match win and improved his win streak to 15.
Nadal will today lock horns with sixth seed Grigor Dimitrov whereas Federer will cross swords with Richard Gasquet of France.
Nadal hadn't won an ATP hard-court title in more than three years until the U.S. Open last month, and now the Spaniard is gunning for his third title in five weeks.
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