Evans had previously reached the third round at Flushing Meadows three times, holding a match point against eventual champion Stan Wawrinka in 2016, but had never made it further.
The 31-year-old arrived in New York low on confidence after a bout of coronavirus left him playing catch-up physically but he has shown why he is regarded as one of the grittiest competitors on tour and goes into Sunday’s clash eyeing an upset.
“I’ve got as good a chance as anyone to do some damage,” said Evans. “I think my game is in a good place. He’s a great, great player, unbelievable competitor, good mover. He’s been playing some unbelievable tennis this year.
“But if I go on the court and think I’ve got no chance and there’s no pressure on me – I think in the pressure situations, if they do arise, you’re not ready for that. You’ve got to go in believing you can win.”
Evans is set to hit a new career-high ranking inside the top 25 by virtue of his run in New York but Medvedev represents a big step up from the opponents the British number one has faced so far.
The Russian reached his first grand slam final at Flushing Meadows in 2019, pushing Rafael Nadal to five sets, and won his fourth Masters tournament in Toronto last month.
“I think his serve’s an amazing, amazing weapon,” said Evans. “His serve and his movement, two of the best things. I think his serve is underrated. He rolls through his service games very quickly. He obviously puts a lot of balls in court on the opponent’s serve. Those three things are probably his best.
“I don’t want to keep going on about how good he is. I think his ranking gives that away.”
Medvedev, who has cruised through his first three matches, returned the compliments to Evans, describing him as a tricky and clever player.
“He doesn’t have one shot that is a weapon, and yet he’s a top player for many years already,” said the Russian.
“The way he chooses the right moment to go to the net, to slice, to make a drop shot. His serve is not huge, but it’s tough to return. Great player. I heard today in the locker room people saying, ‘I love watching him play’. Probably most of us like watching him play.
“I saw that he was two sets down (against Popyrin). I watched a little bit of the fifth set – what a tie-break from him. First time actually playing against him, so never easy. I want to show my best level. That’s how I will have my chances to win.”