Spanish second seed Alcaraz emerged from a tense first set to defeat Russian seventh seed Karen Khachanov 7-5, 6-2 in Beijing.
Serving at 4-4 in the first set, Khachanov eventually held after a gruelling game in which both players gave up multiple game points when Alcaraz put his forehand long.
It was to be only a temporary reprieve.
The 21-year-old Alcaraz had the Russian under pressure once again at 5-5 and this time the world number three made no mistake, grabbing the break and then holding his own serve to go a set up.
Alcaraz, who recorded his 200th tour-level win on Sunday, broke for 3-2 on the way to winning a more comfortable second set.
The Russian third seed Medvedev, who lost last year's final to Jannik Sinner, beat unseeded Italian Flavio Cobolli 6-2, 6-4 in his quarter-final.
Alcaraz and 2021 US Open champion Medvedev have met seven times before with the Spaniard winning five of their meetings, most recently in the semi-finals at Wimbledon.
Alcaraz went on to beat Novak Djokovic in the final and retain his title.
