In the first set, which lasted only 25 minutes, the Italian broke Medvedev in the second and sixth games to murmurs of surprise from the crowd.
The Russian kept holding his shoulder, which he had said the day before had "some niggles", and received medical attention several times during the match.
"I'm obviously very happy. I think we know each other very well... It was a very tactical match," said Sinner.
"It's a great feeling to be in the semis here, it's a very special tournament."
This was the fifth time Medvedev and Sinner have met in the latter stages of tournaments this year.
Sinner beat Medvedev in the semi-finals in Miami, the quarter-finals of the US Open and in the Australian Open final, but the Russian ended the Italian's hopes in the last eight at Wimbledon in an epic five-set battle.
In the Shanghai semi-final, Sinner could meet Alcaraz again after the Spaniard defeated him at the China Open final in Beijing last week.
Alcaraz will later on Thursday play Czech Tomas Machac in the last eight.
