Medvedev took the opening set in a tiebreak as an erratic Alcaraz struggled for consistency, but the Spaniard fought his way back into the contest before wrapping up a 6-7(1), 6-3, 6-4, 6-4 victory.
Three-time Grand Slam champion Alcaraz has spoken in the past about how he sometimes struggles to keep his nerves in check and said he needed to control his emotions against Medvedev in order to keep his Wimbledon title defence on track.
"Obviously having nerves is normal but you have to control it. When you're not controlling it, it's difficult to play your best tennis or to deal with the situations," he told reporters.
"That's what happened in the first set to me. I was struggling with playing my service games calm. I was in a rush. I was nervous. Daniil seemed like he was controlling the match.
"So after that set, even if I lost the first set, I calmed myself and I started to play better, to feel like I'm going to have fun. After that I'm going to play my best tennis."
Third seed Alcaraz will face Djokovic in a repeat of last year's Wimbledon final when the Spaniard triumphed in five sets.
The pair have faced each other five times with 24-time Grand Slam winner Djokovic winning three of their encounters.
"I know how it's going to feel playing against Djokovic. I've played few times in Grand Slams, final of Master 1000, multiple times against him," Alcaraz said.
"I know what I have to do. I'm sure he knows what he has to do to beat me. It's going to be a really interesting one.
"But I'm ready to take that challenge and I'm ready to do it well."
