Djokovic complemented a fine display of serving by converting three of his five break points in a 6-4 6-3 victory, recording his seventh consecutive win after his absence from the US Open.
The 21-time grand slam champion has now reached six semi-finals this year, but saw room for improvement in his performance after beating the world No.18.
"I didn't play as well from the baseline as I did in the first two matches, but still it was enough," Djokovic said. "I managed to produce some good tennis when it was most needed in both sets."
Looking ahead to his final-four match, the Serb added: "I always expect highs from myself. Hopefully I can elevate still the level of my game for tomorrow, because it's going to be needed."
Djokovic will face an 11th ATP Tour-level meeting with Medvedev in the next round after his fellow former world No.1 recorded a dominant 6-1 6-1 win over Roberto Bautista Agut.
On the other side of the draw, No.3 seed Stefanos Tsitsipas beat Hubert Hurkacz 7-6 (10-8) 6-3, and will now face Andrey Rublev after he eased to a 6-1 6-2 win over Adrian Mannarino.