Top seed Alcaraz eclipsed Sinner 7-6 (4) 6-3 in a thrilling encounter that was reminiscent of their epic clash at last year’s US Open.
An early break allowed Alcaraz to gain a 4-2 advantage, however Sinner rattled off three games in a row en route to taking a 6-5 lead.
The Italian had an opportunity to take the first set, but Alcaraz managed to fend off the set point and force a tie break.
That effort signalled a change in momentum for Alcaraz, who claimed the tie break and cruised to victory in the second set, wrapping up the match in an hour and 52 minutes.
American Tiafoe saved seven match points in a spirited ending to the first semi-final but eventually fell to a 7-5 7-6 (4) defeat as Medvedev made it 19 victories in a row.
A win against Medvedev would propel Alcaraz back to world number one after injury brought a premature end to his previous reign on top.
Meanwhile, Britain’s Neal Skupski and Dutch partner Wesley Koolhof fell just short of victory in the doubles final, going down to Rohan Bopanna and Matt Ebden 6-3 2-6 10-8.