The Romanian qualifier does not have a world ranking and is making her first WTA main draw appearance since 2017 after struggling with multiple injuries as well as giving birth to her daughter in the past year.
Tig's week to remember at her home tournament went on with an emphatic 6-3 6-1 triumph over No.6 seed Laura Siegemund.
Tig has only lost one set all week and saved each of the eight break points she faced against Siegemund, winning in 87 minutes.
"It's very, very special to be in the final in Bucharest," the emotional victor, who has beaten three seeded players to reach her first final in four years, said.
Tig, 24, will meet either Elena Rybakina or Martina Di Giuseppe in in the showpiece, the second semi-final having been heavily disrupted by rain.
The final of the Ladies Open Lausanne will see Alize Cornet take on Fiona Ferro in an all-French affair after both players won their semi-final matches in straight sets.
Ferro saw off Bernarda Pera 6-1 6-4 in Sunday's (AEST) opening match to reach a first WTA final, her American opponent failing to register a single break of serve.
No.3 seed Cornet, who won the event last year when it was played in Gstaad, then got the better of Tamara Korpatsch 6-3 6-4 in two sets that by contrast produced 11 breaks.
"I think it's going to be hard and beautiful at the same time," Cornet said ahead of the clash with her compatriot. "[Ferro is] the new generation of the French players, and she's such a nice girl.
"She's a bit like my little sister on the tour, and I like her a lot. It's always tough, especially when you play a friend. But in both cases it's going to be beautiful, because either I win or my friend wins."