Barty is through to her sixth title match of the season – her first in Cincinnati – after beating Angelique Kerber in straight sets in their semi-final.
In action on the WTA Tour for the first time since winning at Wimbledon, having gone to the Tokyo 2020 Olympic Games in the intervening period, the Australian came through a sloppy spell in the second set to advance 6-2 7-5.
Teichmann is next, taking on Barty for the first time after a stunning run continued with victory over Karolina Pliskova.
The world No.76 had already eliminated Naomi Osaka and Belinda Bencic and was a deserving 6-2 6-4 winner against Pliskova.
Barty had been racing towards victory when she took the opener on Kerber's serve, her second break, and then went 2-0 up in the second.
But Kerber gave the favourite a scare by winning each of the next three games, belatedly finding joy against the Barty serve.
The Wimbledon champion has won more matches than any other player on the WTA Tour this year, though, and regained her composure to break twice more for a 39th triumph of 2021.
"It's never, ever a walk in the park against Angie," Barty said. "She's an exceptional competitor and I think early on in that second set she went to another gear and it took me a few games to go with her.
"That was the change – she was able to lift her game and, even though there were some close games, she won the big points early on in the second set.
"I'm glad that I was able to find a way through there in the end.
"I had to find the balance of being aggressive and not getting too passive and letting Angie dictate.
"She moves exceptionally well, puts the balls in difficult positions, and I felt like when I was able to control the court I did a better job.
"In the games I got broken, she just saw too many second serves and was able to be assertive.
"I'm really happy to get through in the end, and to be playing for a title here in Cincinnati is awesome."
Despite facing three seeded players in succession, Teichmann has not dropped a set since losing the first against Osaka in the Round of 16.
Continuing that sequence against Barty will be a tough ask, but few would have anticipated Pliskova being brushed aside quite so easily.
Teichmann herself has no explanation for a sensational run of form.
"It's tough to explain," she said. "When I ask my coaches what they think of me, they always say, 'You're just an unexpected person, you do random things', so I guess that's one of them.
"I'm feeling really, really good here, the conditions, serving good, moving well, when I can I attack, I defend ... What I'm feeling here, I cannot even describe it.
"It's a dream. I'm playing centre court, a final against the world number one. I cannot ask for anything else."