Dimitrov, the 11th seed, utilised his forehand to devastating effect throughout the match, making just three unforced errors to take the first set.
Fourth seed Zverev, however, regained some control in a tight second set, serving with accuracy to deny Dimitrov any opportunities to break before clinching the tie-break to level the match.
Dimitrov took his tally of winners up to 44 in the decider as he defended a break point and then took the lead at 4-3, before confidently settling the match on serve for his first win over Zverev since 2014.
"It was like a dogfight on both ends, we really went after each other," said Dimitrov, whose victory will see him return to the top 10 for the first time since 2018.
"He upped his game in the second set, in the third set he also had a chance but I served well."
In Sunday's final, Dimitrov will face Sinner, who powered past defending Miami Open champion Daniil Medvedev 6-1 6-2 to reach the final for the second year in a row.
Dimitrov will climb back into the top 10 for the first time since 2018 after beating Zverev, and the Bulgarian says he is finally reaping the rewards of his hard work.
He had been touted as a potential winner of the biggest prizes in tennis since becoming Wimbledon junior champion in 2008 with a style likened to that of Roger Federer, but the 32-year-old has yet to live up to his early promise.
However, he has been in fine form in recent weeks, defeating top-10 players Carlos Alcaraz and Hubert Hurkacz in Miami before his win over world number five Zverev in the semi-final.
"I think the consistency of beating top players, that to me is a bigger success than anything else," Dimitrov told reporters after his win.
"If you do that, you get the ranking. If you do that, things are just getting better for you... I think the discipline brought me to this moment. There is nothing else. I didn't kind of deviate from my target.
"I had small targets throughout - every single week I had a target, and also to be able to put my body through all that on a daily basis was also very important for me. When you start putting all that together, I think it's what I'm most proud of."
Dimitrov said he is hoping to employ his diverse array of skills to the best of his ability against Sinner.
"I know I have a lot of tools in my bag that I can use, but also I need to make sure that I use them at the right time," Dimitrov said.
"I think today, for example, I was able to, especially in the third set, I was able to use those ones, you know, the finesse, use the slice a little bit more, be a little bit more aggressive with my forehand, serve and volley, coming in."
