It was midway through the second set when he was standing behind the baseline, his sweat turning his dark-blue shirt several shades darker as he tried to catch his breath.
The man on the other side looked like he was having a day at the beach.
The Russian would have regained the top spot in the world rankings if he had prevailed in the quarterfinals. Hurkacz moved two wins away from defending his Miami Open title by defeating the top-seeded Medvedev.
Hurkacz said that he was putting pressure on his serves and that helped his game.
Hurkacz will face either Carlos Alcaraz of Spain or Miomir Kecmanovic of Serbia in the semifinals.
The other semifinal features an unseeded man against a sixth-seeded man.
Hurkacz and Medvedev have met four times, and each of them has ranked in the top 2 in the world. Hurkacz is 12-1 all-time in Miami, and he improved to 14-5 this year.
Hurkacz said that coming here is so much fun.
Unseeded Naomi Osaka will face No. 22 seed Belinda Bencic in the women's semifinals on Thursday.
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