The British number two is through to the third round at Flushing Meadows for the sixth time in his career after a four-set win over Dutchman Botic van de Zandschulp.
His ‘reward’ is a match-up with 20-year-old Spaniard Alcaraz, who picked up his first grand slam title in New York last year and added the Wimbledon crown earlier this summer.
Evans, seeded 26, said: “It’s a little annoying to have him in the top eight of the draw but it is what it is.
“It will be a good match. I am really looking forward to it and will play aggressively.
“It’s a very difficult draw. He will obviously be the overwhelming favourite but it’s a good opportunity to play a very good tennis player on a big stage. That is why you play tennis.”
Alcaraz has won both of their previous two meetings in straight sets, but Evans boasts a better record on the golf course after the pair played a few holes at Wimbledon.
“Of course, his golf is much better than mine, that’s for sure,” said Alcaraz. “We played a little bit before Wimbledon. We had such a great time at the course.”
Katie Boulter has reached the third round of an overseas grand slam for the first time and is on the brink of breaking into the world’s top 50.
The 27-year-old from Leicester faces Peyton Stearns, a young American who she lost to in three tie-breaks in a marathon match in Austin, Texas, in February.
“I actually played probably the longest match of my career against her in Austin this year,” she said. “It was a 7-6 in the third, five in the tie-break loss. It was a brutal match. Three hours and 25 minutes.
“I’m expecting a lot. I mean, she’s a real talent. She’s a great player. The courts suit her a lot here.
“Again, I know it’s going to be physical and I’m going to have to be ready and playing some of my best tennis to beat her.”
British number one Cameron Norrie has what looks like another winnable tie against Italian world number 61 Matteo Arnaldi.
But if he gets through, the 28-year-old will run into Alcaraz – or Evans – in the fourth round.
Jack Draper, who brilliantly accounted for 17th seed Hubert Hurkacz on Thursday, faces American Michael Mmoh.