Paul, the 14th seed, is the first American to reach the final four at the Foro Italico since Reilly Opelka in 2021.
The momentum-shifting quarter-final came down to the wire, with a 15-minute final game capping off nearly two and three-quarter hours on court.
Paul finally came through on his fourth match point as Poland's Hurkacz sent a return long.
The match featured 13 breaks of serve, with Paul advancing with 29 winners and 41 unforced errors; and Hurkacz having 22 and 44 respectively.
"I started well but it got away from me in the second and start of the third," Paul said. "I had to stick around in the match.
"I found the energy to get it going again. I was hitting my forehand bigger and with more intensity because Hubi can really crush the ball."
Hurkacz, who knocked Rafa Nadal out in the Rome second round, was unable to get his massive serve up to speed as he faced Paul, winner over defending champion Daniil Medvedev in the fourth round.
Hurkacz won the clay title in Estoril last month and suffered only his third loss on clay this spring.
Paul will next face Chile's Jarry, who came from behind to stun sixth seed Tsitsipas in the final men's quarter-final in Rome.
Jarry was tested in the opening set by the Greek but gained his momentum in the second.
He won five consecutive points at 3-3 as he bounced back from 0-40, before wrapping up the second set by winning nine of the final 11 points.
Jarry then broke Tsitsipas in the decider for a 5-4 lead to eventually cruise into the last four.
"Beating Stef on clay is a good achievement. Extremely happy for my fight today and how I played. How I maintained myself even down a set, down a break," Jarry said.
"I just kept trying to find different ways to have chances on his serve. I knew I was playing good.
"I had to adjust some things on the backhand so he didn't push me back. That's why he played so good. I was able to do those two things... It was a good fight tonight. Hopefully tomorrow I can be stronger."
Another Chilean, Alejandro Tabilo is already into the other semi-final and will take on German third seed Alexander Zverev.
