Hurkacz, seeded 26th, has won three in a row when facing a top-five opponent, but he beat Tsitsipas for only the second time in their eight meetings.
"I just try to like keep building my game and improving," Hurkacz said. "Not all the time are you going to have the results that you want, but if you stay positive and improve your game, the results will eventually come."
The upset further scrambled the draw. Novak Djokovic, Rafael Nadal and Roger Federer skipped the tournament, and No. 1-seeded Daniil Medvedev lost in the quarterfinals Wednesday night to No. 7 Robert Bautista Agut.
In the last quarterfinal Thursday night, unseeded 20-year-old Sebastian Korda's breakthrough run ended with a quarterfinal loss to No. 4 Andrey Rublev, 7-5, 7-6 (7). Korda, slowed in the second set by a left thigh injury, was the youngest American to make the men's quarterfinals in Miami since Robbie Ginepri in 2003. Korda said he didn't think his injury was serious.
"This week showed me I can keep up and play with the biggest names in tennis," Korda said. "It was a really positive week."
Bautista Agut will face No. 21 Jannik Sinner in the first semifinal Friday, Rublev and Hurkacz will play in their first semifinal at a top-level ATP event when they meet Friday night, and a first-time ATP Masters 1000 champion will be crowned Sunday.
"Maybe I feel extra pressure, because I'm the one left who's in the top 10," Rublev said. "But everyone can win now. All of them are playing good tennis."
Hurkacz was serving at 0-2, 15-40 in the second set when he began his comeback. He steadied his baseline game, while Tsitsipas became increasingly erratic and frustrated as the match progressed.
"I was very stressed these two weeks," Tsitsipas said. "I felt like it was my opportunity. It's a very disappointing loss. Everything was under control. And suddenly, I don't know, self-explosion."
Hurkacz hit 15 aces and saved 10 of the 13 break points he faced. He'll climb in next week's rankings to at least 27th, a career high.
"I want to be as good as I can," Hurkacz said. "Hopefully, I can win some titles in the future."
The Associated Press contributed to this report.