The British No2 came from a set down to beat big-serving Dutchman Botic van de Zandschulp 1-6, 6-1, 6-3, 6-3 to reach the third round in New York for the sixth time.
As the No24 seed, Evans could have drawn any of the top eight seeds but said he would just have to throw everything at Alcaraz.
“It’s my fault (because of his ranking),” Evans said. “It’s a little annoying to have him from the top eight, but it is what it is. It will be a good match. I am really looking forward to it and will play aggressively. There’s been a few upsets on that court before.”
Evans said he would take some heart from the fact he has faced Alcaraz twice, even if the Spaniard won contests both in straight sets.
“I played a good match in Barcelona this year and have some insight into how he will play,” said Evans. “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.”
After losing in the first round at Wimbledon this year, Evans found form on the US hardcourts, winning his biggest title to date as he took the tile in Washington last month.
That performance, in similar conditions, helped Evans against Van de Zandschulp, the world No65, after a difficult first set on a rowdy Court 11.
“I played in these conditions late at night a lot in Washington,” said Evans. “They are very similar here. I felt comfortable to be able to lean on that.
“On big points on second serve I know I have made a lot of them under pressure this summer in America and vice versa when I am break point down or break point up. When I don’t it’s no big deal. Go back and work for the next point.”
Evans has British company in the third round of the men’s draw on Saturday after impressive straight-set wins for Cameron Norrie and Jack Draper.
Norrie beat Yu Hsiou Lu of Taipei 7-5, 6-4, 6-4, while Draper upset No17 seed Hubert Hurkacz, of Poland, 6-2, 6-4, 7-5 to equal his run to the third round last year.