The game, which took place in Madrid, ended with a score of 6: 4, 6: 4 in favor of the 25-year-old Muscovite.
The meeting lasted 1 hour and 12 minutes.
Medvedev ranks second in the ranking of the Association of Professional Tennis Players (ATP).
A little earlier, Andrei Rublev outplayed Elias Imer.
The score in the match was 2: 0 in favor of the Russians.
Russia will play with Germany in the semifinals of the tournament.
Earlier, Rublev commented on his victory in the opening match of the Davis Cup quarter-finals in tennis over Elias Imer from Sweden.