Medvedev, who won the tournament in 2023, scored his first victory over a top-30 player in 2025.
Medvedev, the former world number one, has not won a tournament since the Rome Masters in spring 2023. He was knocked out in the second round of this year's Australian Open by teenage American Learner Tien.
In a match of long rallies, Medvedev did not carve out a break point until the 12th game of the second set, by which time he was a set down. He took his chance and then went on attack in the third set to win in two hours 30 minutes.
A third Russian former champion, Andrey Rublev, the fifth seed, beat Alexander Bublik 6-3, 6-4.
Alex de Minaur celebrated his birthday by beating Russian Roman Safiullin 6-1, 7-5, even though the Australian did not enjoy the weather.
"They're tough days, these ones," said De Minaur. "It's cold, it's windy, you probably don't want to get out of bed. But once you step on court, you have to do everything you can to win. Whether it's ugly or pretty tennis, you just put the ball in the court, and that's what I did today."
"Out went any sort of tactics you had for the match and it was all about surviving more than anything."