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Italy's No. 1 Sinner produced a devastating display to outclass a helpless De Minaur after Matteo Arnaldi outlasted Alexei Popyrin in the first singles clash.
The two players have conveyed their unavailability for the World Group I play-off tie to be played in February but have not specified the reason behind their decision.
A sell-out crowd in Turin's Pala Alpitour had hoped to cheer the 22-year-old Sinner to the biggest title of his career but Djokovic was simply in a different league.
The 20-year-old Alcaraz, who also has won six titles this season, missed out on becoming the youngest finalist in the season-ending tournament since Pete Sampras in 1991.
Alcaraz will face Green Group runner-up Novak Djokovic in a mouth-watering semifinal.
Home favourite Sinner also clinched top spot in the group with a 3-0 record.
The 20-year-old Alcaraz will need to beat Medvedev in his final group game on Friday.
The earlier Green Group clash was a non-event as Stefanos Tsitsipas retired injured against Holger Rune.
Rublev, ranked fifth in the world, began to despair after losing the first set and failed to put up much of a fight in the second.
Jannik Sinner made a dream start in front of his home crowd with a 6-4, 6-4 defeat of Stefanos Tsitsipas in their opening Green Group clash.