It is the fifth time in the past six years that Medvedev has reached the last eight at Flushing Meadows.
The fifth seed was broken just once in the match, as he went down 2-1 in the third set, before play was delayed after a fire alarm went off in the building where the electronic line calling team is.
The US Open does not have line judges, with all the calls made by the Hawkeye technology.
The building was evacuated, leading to a brief pause in play, before fifth seed Medvedev immediately broke back and won five of the next six games to advance.
Medvedev was interviewed on court afterwards by Nick Kyrgios, who was the last player to beat him before the quarter-final stage in New York.
“The last time I lost in the fourth round was against you, right? Good memories,” the 28-year-old joked.
“I try to work hard. Sometimes I do, sometimes I don’t.
“I have the mentality that if the other guy practises more than me, I have less chances to win, and I want to win all the time.”
Britain’s Jack Draper earlier advanced with an impressive straight-sets victory over Tomas Machac to reach his first Grand Slam quarter-final.
He will play 10th seed Alex de Minaur in the next round after the Australian beat compatriot Jordan Thompson 6-0 3-6 6-3 7-5.
After De Minaur breezed through the opening set in just 29 minutes without losing a game, Thompson hit back to take the second and ensure the remainder of the match was far more closely contested.
De Minaur secured the win after a topsy-turvy fourth set to become the first Australian man since Leyton Hewitt in 2004 to reach three consecutive Grand Slam quarter-finals.
Related News :