Casper Ruud maintained the pace with his 31st match win of the season to reach the Madrid Masters fourth round with a 6-2, 6-4 win over Brit Cam Norrie.
The Norwegian – titleholder this month in Barcelona – has won 11 of his past 12 matches to lead the Tour in season victories.
It took 80 minutes to dismiss Norrie, with Ruud rallying from a break down in the second set
Fourth seed had to battle to defeat Sebastian Korda, producing a 5-7, 7-6(4), 6-3 result after standing two points from an exit.
The winner overcame 24 unforced errors in the up-and-down win over the American in just under two and a half hours.
“It was tough for many different reasons,” Medvedev said. “The courts here except the central court are a bit smaller than I would like, so I play like someone is pushing me in the back.
“But if you win matches you are happy.”
The fourth seed now faces Alexander Bublik, as the Kazakh beat Ben Shelton 3-6, 7-6(2), 6-4.