The meeting lasted 1 hour 20 minutes and ended with a score of 6:3, 6:3 in favor of the seventh racket of the world.
The 24-year-old Russian is the reigning champion of the tournament.
In the quarterfinals, Rublev will play either the Dutchman Tallon Grikspor or the Hungarian Marton Fucovich.
Earlier it was reported that Karen Khachanov could not reach the 1/4 finals of the tennis tournament in Rotterdam.