The second seed will face world number one and defending champion Jannik Sinner or Chinese wildcard Bu Yunchaokete for the title.
Spaniard Alcaraz is into his first final in Beijing, something legendary compatriot Nadal did four times.
Alcaraz, looking to bounce back from a second-round exit at the US Open, drew first blood when he broke last year's finalist Medvedev for 3-2 in the first set.
Alcaraz looked in the mood, cupping his ear to a capacity crowd after emerging from one scintillating rally.
They then failed to hold serve for three games in a row, leaving the set poised at 4-4.
Third-seeded Medvedev became increasingly frustrated after a couple of calls failed to go his way and Alcaraz broke for 6-5, then held to wrap up the set in 48 minutes.
Alcaraz broke for a 3-2 lead in the second set, after which Medvedev had treatment from the physio on his left leg.
He had more treatment at 3-4 down as his hopes slipped away, Alcaraz getting the job done on his fourth match point.
Alcaraz is one win away from his 16th ATP Tour title.
The final is on Wednesday.
