The world number one had lost four of five previous matches against the German, with his only win coming at Roland Garros four years ago.
The tight victory took more than three hours not including a rain interruption.
The match was paused midway through the first-set tiebreaker for nearly 30 minutes while a shower passed over the area -- another episode of the poor weather which has plagued the event in recent days.
Sinner saved two Zverev set points and won the opener on his own third chance, only to fall in the second set as he lost an early break and was broken again in the 12th game as he sent an overhead into the net.
The third set went into a tiebreaker with Sinner taking a 5-2 lead and triumphing on his second match point.
"It was a tough match, a very exciting match," the Italian said. "We played in different conditions: sunny, rain and then night.
"There was a lot of tension for both of us. I'm very happy with my performance and happy to be in the final."
Sinner, who won his last title on grass in Halle two months ago, will play a rare Monday final against the winner from Frances Tiafoe and Danish 15th seed Holger Rune.
"I had to play with my gut, I feel that is my strength," the 23-year-old said. "We had some ups and downs over three hours."
"I couldn't have played a better match than this to prepare," he said, looking ahead to the start of the US Open in eight days.
The player who has suffered recently with a hip problem, illness and the tonsillitis which forced him to skip the Olympics, said he needs to keep up his fitness.
"If I'm going to win bigger matches, I have to be more in shape. Today I stayed mentally strong; I'm proud of that."
Sinner will be playing in his fifth career Masters 1000 final.
Crazy
Tiafoe came from 5-2 down in the final set and claimed a tiebreaker for a 4-6, 6-1, 7-6 (7/4) defeat of Danish 15th seed Holger Rune.
Tiafoe is the first American man to play the final here since John Isner in 2013; he saved two match points in his come-from-behind win.
Tiafoe will move into the ranking top-20, joining four compatriots in the strongest US showing since 1997.
"It was crazy, that last set was nuts," the American said. "It got breezy at the end, but you just had to play the percentages.
"I got lucky with a couple of net cords, which made a huge difference. I battled in the tiebreaker and he got a little tight. One thing led to another and here we are."
Tiafoe said that even trailing 5-2, "I was not too stressed. I just put the pressure back on him. You have to make him beat you."
