The 52nd-ranked Aussie hammered 19 aces, saved a match point and often played to the crowd in a dramatic and emotional 6-4, 3-6, 7-6 (9/7) victory over Tsitsipas, whose broken shoes caused two third-set delays.
Tsitsipas, who becomes world number five on Monday, fell behind a set and a break, took advantage of Kyrgios losing control with racquet slams and call complaints to force a third set, only to fall in the tie-breaker.
"It was spiraling out of control at one point," Kyrgios said. "I've been in that spot before and it has gotten worse.
"I'm pretty proud at how I was able to drag it back from a dark place. I'm pretty proud of how I battled back and dug deep."
Kyrgios will play for the $365,390 (328,851 euro) top prize against 10th-ranked Russian Daniil Medvedev, who eliminated German lucky loser Peter Gojowczyk 6-2, 6-2.
The 24-year-old Aussie beat Medvedev this year in Rome in their only prior meeting.
Kyrgios, who improved to 4-1 against top-10 rivals this year, seeks a sixth career ATP title and his first since Acapulco in March.
"It's probably one of the best tournament weeks of my life," Kyrgios said.
Medvedev, 23, seeks his fifth ATP title after taking his most recent crown at Sofia in February.
Italy's 62nd-ranked Camila Giorgi, a 2018 Wimbledon quarter-finalist seeking her third WTA title, and 79th-ranked American Jessica Pegula advanced to the women's final at the US Open tuneup tournament.
- Kyrgios fire and apathy -
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Kyrgios excited the crowd throughout with such flamboyant moves as underhand serves, between the legs shots and leaping drop shots. Other times he would just swat away.
"He was on fire in some moments," Tsitsipas said. "It felt like sometimes he didn't care at all. It's probably his plan to put you out of focus."
Kyrgios admitted, "I've always been able to play high level tennis. I just need to be more consistent. I have to be mentally tougher."
It was the Greek star's first match against Kyrgios, who is of Greek and Malaysian heritage. Each man won 91 points, hit 58 of 91 first serves, won 48 of 58 first-serve points and 16-of-33 second serve points.
"I'm an anti-stat guy," Kyrgios said. "I don't look at any of that stuff."
Kyrgios broke in the third game and held from there to win the first set in 31 minutes, dropping only three points on his serve.
"His serve was just unreal first set. I couldn't do anything with it," said Tsitsipas. "I haven't seen anything like it."
Kyrgios broke again to open the second set but after a review call went against him double-faulted away a break, slamming his racquet and towels to the court in frustration.
- 'Shoe-pocalypse' hits -
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Tsitsipas, who said he had a sore hamstring, suffered a broken left shoe for a fourth consecutive match, switching Adidas pairs on a changeover with Kyrgios up 2-1.
A ballboy delivered a shoebox with the faulty footwear to Tsitsipas's father/coach, Apostolos Tsitsipas, in the stands. But it was Kyrgios, waiting through a delay that would last four minutes, who took the shoebox from the far corner of the court.
"I just thought it would speed the process up," Kyrgios said. "By the way, Adidas sucks."
Kyrgios delivered it to a seated Tsitsipas, kneeling as he put the box at his rival's feet, both of them smiling as the crowd roared with delight and laughter.
"That was funny," Tsitsipas said. Sometimes you can't take anything serious. You have to go with the flow. You have to have the same channel and same fun as he is."
Tsitsipas broke another left shoe and needed another shoe switch at the next changeover, Indian tennis legend Leander Paes later bringing his dad a new shoe later.
Kyrgios led 5-1 in the tie-breaker, lost the next five points, then saved match point with a service winner. He finally won after two hours seven minutes on an overhead smash.