Evans had lived up to his 25th seeding by reaching the third round and went into the match as the underdog but had reason to believe he could cause an upset having won three of his six previous clashes with Rublev.
However, the Russian crunched 60 winners compared with only 22 unforced errors in a quality display to win 6-4 6-2 6-3 and leave Andy Murray as the only British singles player remaining ahead of his meeting with Roberto Bautista Agut later.
There is nothing subtle about the game of Rublev, he simply hits the ball as hard as he can, especially off the forehand, but he has done it consistently enough to stay in the top 10 for virtually the entirety of the last two years.
Evans spends much of his time feeling like he is competing in a higher weight category as one of the smaller players on tour.
Speaking after his second-round match, he said: "Everybody's dealt the cards. I'm sure some people would like to have a bit more skill and feel. I'd like to have a bit more power. It is what it is."
The 32-year-old did a good job of dealing with the big blows coming from the other end during the first set, and a backhand fizzed up the line in the seventh game gave Evans a break point.
But Rublev saved it and, when the Russian created a set point at 4-5, this time Evans netted.
Rublev, who has come as close as any of the Russian male players to criticising the actions of his home country, was taunted by several fans prominently displaying a Ukrainian flag during his previous match.
There was no repeat of that here and little to unsettle him, with Evans broken from 40-0 as Rublev opened up a 4-2 lead in the second set.
Rublev was playing better and better, pushing Evans well behind the baseline and offering the British player only a few crumbs in terms of errors.
Evans continued to battle but, although he saved three set points at 2-5, Rublev took the fourth and then opened up a 3-0 lead in the fifth.
Evans had to save five break points just to stop the run of games against him at seven, and Rublev avoided any late hiccups, clinching victory after two hours and nine minutes.