Rublev indeed enjoyed a fast start to their match following Aryna Sabalenka’s victory over Zheng Qinwen, who downplayed the conditions in her post-match press conference. With the Ashe roof partially closed, the 25-year-old had the advantage of playing without full sun, but the humid conditions were palpable as Medvedev worked his way into the match.
"When he started the match, I think he won 10 points in a row and hitting on the line," Medvedev said. "I was like, 'Okay, I'm going to have to be better than I am right now.' It was the same pretty every match. De Minaur threw me off the court 6-2. So I was like, 'Okay, I need to be better.'
"That's what I'm really proud of. Sometimes it's not easy to come back in the matches, to stay there with the tough conditions. Andrey and Alex are probably one of the best physical guys on tour, and I managed to make them suffer. I suffered myself also but I managed to make them suffer. All of this is good for the confidence. Is good for next matches."
The No. 3 seeded-Medvedev, who dealt unruly crowd behavior earlier in the week, reeled off six of seven games from 0-3 down, and pulled off a similar Houdini comeback in the second to put himself a set from the semifinals.
Rublev saved his deepest push for the third when he emerged from another exchange of breaks to put himself up 4-2 as a frustrated Medvedev quipped of the heat, "One day, a player's gonna die, and then you'll see." Medvedev would nonetheless come back from there, winning the next three games and saving a break point in an extended ninth game.
"Maybe I'm going to finish my career and nothing is gonna happen and then it's fine, then I'm talking for nothing," said Medvedev, "but the question is we don't want something to happen and then say, Oh, my God, Medvedev said this a couple of years ago.
"I don't have real solutions but it's still better to speak a little bit about it before something happens," he added.
Serving to stay in the match, Rublev missed forehand long up game point while Medvedev tracked a drop shot to earn his first match point. Rublev saved two with some strong serving and two others with audacious shotmaking from the forehand, but a forehand wide pulled up a fifth opportunity for Medvedev to make the semifinals.
Medvedev played impeccable defense when it mattered most, drawing one last error from his rival to edge over the finish line in just under three hours.
"If I compare myself to two years ago, I would say definitely not worse," said Medvedev. "It was enough two years ago. But to me, to continue this way, two more matches to go."