No.2 seed Safarova needed almost an hour and thirty minutes against Germany's Carina Witthoeft before battling through 6-4, 6-3 and reach her first WTA final since April 2016 in Prague.
"I knew Carina was playing very well, I knew I had to be tough out there and that is what I did," Safarova told wtatennis.com after the match. "Probably experience helps, I was called a veteran on the WTA, I don´t feel like that but it was a good match.
"I am very pleased with being in a final after a long time."
She'll face a tough challenge in the final against Hungarian No.1 Babos, whom she teamed up with for doubles this week, reaching the quarterfinals together before Safarova was forced to withdraw with a right thigh injury.
Under the watchful eye of former World No.1 Monica Seles, top seed Babos overcame a tense opening set against Julia Goerges, the No.3 seed - she was unable to convert on three break point chances - including a set point - before finally edging through 7-5.
"Julia is a very very good player, a very experienced player on tour, so I knew it was going to be a tough one," Babos said after the match.
"Honestly, I was a bit afraid in this match, and you could tell in the first set that I didn't take all my opportunities. But after this, I got a little bit more into it, you could say I got mad at myself, and tried to play really aggressive and it worked out pretty well."
Goerges was all business in the second, going up a double break to close out the 7-5, 6-1 victory in an hour and twenty minutes to reach a WTA final in her home country for the first time.
"I had a tough beginning of the year, and was just really trying to stay positive and keep my head up. Being at home, in front of this crowd and showing my emotions - this is what I was waiting for. Budapest has really turned around my season."