The match concluded with a scoreline of 7-6 (7/2), 3-6, 6-4.
Notably, Gauff, who is 19 years old, managed to break her streak of seven consecutive losses against Swiatek.
This victory came after a competitive battle lasting nearly three hours, during which Gauff seized her first win against the formidable Polish player, saving four match points along the way.
“I knew playing her was going to be tough,” Gauff said. “I really took my opportunities when I got them and I really just fought every point.
“I was a little bit negative in the second but I got it back and I was telling myself, ‘You’re a warrior and you can do this.'”
Swiatek had not dropped a set in sweeping her prior matches against Gauff, who will play Sunday for the title on Sunday against either second-ranked Aryna Sabalenka or Czech Karolina Muchova.
Gauff became the first teenager to reach the Cincinnati final since Vera Zvonareva in 2004.
“I tried to serve as hard as I could on the match points,” Gauff said. “She is number one in the world — you have to focus on your end of the court.”
Gauff said her game felt strong on the day.
“I was playing a little bit better today. It came down to the wire,” she said. “It was nice to play in front of an American crowd, even if there were some Polish flags in the stands.”
Gauff’s triumph was her 11th career victory over a top-10 opponent. She beat 10th-ranked Wimbledon champion Marketa Vondrousova last week in Montreal.
“I’ve been working hard and I guess it’s paying off right now,” Gauff said. “I told myself I can let this crush me or make me rise and I decided to make myself rise. It just shows I can do it.”
Swiatek had defeated Gauff twice this season, in Dubai and Roland Garros.
“I was just saying, ‘I’m Coco Gauff and I can do it,'” the teen said. “Playing her, you have to give it your all and I felt it from the moment I stepped onto the court, that I wasn’t going to lose this match today even when the moments got tough.
“And I was right.”
Gauff earned early satisfaction by winning her first-ever set against Swiatek with an opener that ran for 67 minutes.
The set featured four consecutive breaks midway through, with Gauff managing to take it into a tie-breaker.
The American ran off a 4-0 lead and converted on the first of her four set points as Swiatek sent a return long.
But the top seed replied quickly, breaking for 2-1 and again in the final game to square the match at a set apiece.
In the third, Gauff took the lead with a break for 4-3 and finally earned victory as Swiatek volleyed wide on her opponent’s fourth winning chance.
(With inputs from AFP)