The No. 2 seed from Russia dropped a set for the first time in the tournament but recovered to keep alive his bid for a first Grand Slam title.
“Just want to do a little bit better than last two times and get this last step, which is the toughest one actually,” Medvedev said.
His match Tuesday couldn’t have started much easier. He broke six times in Van de Zandschulp’s first eight service games and won the second set in just 22 minutes.
Van de Zandschulp, a 25-year-old from the Netherlands, was trying to become the first man to come through the qualifying rounds to reach the US Open semifinals but was completely overmatched early, disappointing his orange shirt-wearing fans inside Arthur Ashe Stadium.
Van de Zandschulp, who had never even been to New York before the US Open, was attempting to become the first man to reach the semifinals in his tournament debut since 1948.
The quarterfinal Tuesday night between Alcaraz and Auger-Aliassime was the youngest matchup so late in a Grand Slam tournament since 20-year-old Nadal beat Novak Djokovic, 19, in the quarters of the 2006 French Open.