It is Medvedev’s fifth time in six years that he has reached the quarterfinals at Flushing Meadows.
The fifth seed suffered just one break in the match, falling 2-1 down in the third set, before play was delayed after a fire alarm sounded in the building housing the electronic line call team.
There are no line judges at the US Open, and all decisions are made via Hawk-Eye technology.
Play was briefly halted as the building was evacuated, but fifth-seeded Medvedev immediately bounced back, winning five of the next six games to advance to the next round.
Medvedev later had an on-court interview with Nick Kyrgios, the last player to beat him, ahead of their quarterfinal match in New York.
“The last time I lost in the fourth round was to you, right? That’s a good memory,” the 28-year-old joked.
“I try to work hard. Sometimes I work hard, sometimes I don’t.
“I have this mindset that if someone practices more than me, my chances of winning decrease, so I always want to win.”
Jack Draper of England previously developed: Impressive straight set win He defeated Tomas Machak to advance to his first Grand Slam quarterfinal.
He will next play 10th seed Alex de Minaur, who beat Australian Jordan Thompson 6-0 3-6 6-3 7-5 in the next round.
After de Minaur won the first set without dropping a game in just 29 minutes, Thompson fought back to win the second set and the rest of the match was much more intense.
De Minaur secured the win in a tough fourth set, becoming the first Australian male player to reach three consecutive Grand Slam quarter-finals since Lleyton Hewitt in 2004.