The second-ranked Alcaraz, who beat Djokovic in the Wimbledon final, is making his debut at the season-ending event for the year’s top eight players. He missed last year’s ATP Finals because of an abdominal injury.
Medvedev also qualified for the semifinals and will next face Jannik Sinner.
Alcaraz leaned back and yelled in celebration after Medvedev hit a backhand long on match point. He shouted “vamos, vamos,” Spanish for “come on, come on,” as he clenched his fists.
“I had to stay strong mentally. I was struggling a little bit on serve, and his return game is amazing,” Alcaraz said on court. “I stayed calm and strong.”
Djokovic won the most recent meeting with Alcaraz in the final of the Cincinnati Open in August.
The Associated Press and Reuters contributed to this report.