The Chilean, seeded 21st, is the first player from his country to reach a Masters 1000 final since Fernando Gonzalez in Rome in 2007. He will also move up in the world rankings to 17th.
"I think I played my best tennis. I gave it everything and went for it. I did that the whole match. It's hard to keep that level of concentration, but now I'm in the final," Jarry said.
Jarry produced a relentless display of power, hitting 13 aces and 35 winners from the baseline to dispatch Paul in two hours and 44 minutes.
"It was hard to enjoy it. I tried anyway. The important thing is that I came back with my best tennis in the third set and was aggressive. It's never easy to finish, but I did it and it's amazing the feeling I have now," Jarry added.
Jarry, who beat sixth seed Stefanos Tsitsipas in the quarter-finals, will meet Germany's Alexander Zverev in the final on Sunday.