Thiem saves five match points to reach first final since 2020
The Austrian came through 7-6 (7/3), 5-7, 7-6 (10/8) after three hours and 30 minutes, saving all 12 break points he faced against his Serbian opponent.
He will face Sebastian Baez of Argentina on Saturday for the title.
Thiem, a former world number three, is now down at 116 in the rankings after a lengthy battle to overcome a wrist injury which sidelined him for nine months from June 2021 until March 2022.
His last championship match on tour was at the season-ending ATP Finals in 2020.
That was in the same season he captured his only Grand Slam title at the US Open. His victory in New York was his 17th career trophy and most recent.
"I don't know if I can still produce some good words," said Thiem who saved three match points on serve at 5-6 in the third set and another two in Friday's decisive tie-break.
"It was probably the longest best of three match I've ever played in my life, including when I was a kid."
He added: "It was a very tough and intense match. So close every set, every single game."
Thiem, who was the Kitzbuehel champion in 2019, can return to the world's top 80 if he triumphs on Saturday.
"It's very special today, my first final on the tour since my wrist injury. I couldn't be happier that it's here in Austria at home," he added.
World number 72 Baez made Saturday's final by seeing off fellow Argentine and top seed Tomas Martin Etcheverry 7-6 (7/5), 3-6, 6-4.
The 22-year-old arrived in Kitzbuehel with just one win in his previous five tournaments.
"I'm very happy, because the last weeks I didn't have big results, so happy to be in the final," said Baez who defeated Thiem in their only previous meeting at Bastad in Sweden last year.