The Pole came back from two sets to one down to win.
The 24-year-old from Poland came from two sets to one down to win their rain-interrupted fourth-round match 2-6 7-6 (2) 3-6 6-3 6-3.
The match was the only one in the singles draw to become a casualty of the weather on ‘Manic Monday’, having started on Court Two.
They resumed under the roof on Centre Court with Medvedev 2-1 up and on serve at 3-4 in the fourth.
But Hurkacz, the 14th seed, immediately took the initiative by breaking in the first game and levelled the match with an ace.
With Medvedev not looking himself at all, Hurkacz broke him to love for 2-1 in the decider and clinched the match on Medvedev’s serve when the Russian tamely volleyed into the net.
Hurkacz said: “Playing on this unbelievable court, probably the best court in the world, with this magnificent crowd, is so special. It really means a lot to me.
“We were out on Court Two and then came in here. Being here and being able to win that match is so big for me.
“Stopping yesterday in the fourth set was a first for me. I worked with my coach and physio to prepare for today and try to do things better. I think I did a pretty good job today.”
Wroclaw-born Hurkacz decided to take up tennis as a youngster after watching Federer.
“I think Roger, for this sport, is unbelievable. The way he plays, the titles he won,” he added.
“But you guys enjoy watching me as well so it’s going to be fun. I hope I’ll get a bit of support as well.”