Liutova, ranked 229th in the world, will be the youngest player to contest a WTA final since American Coco Gauff in Austria in 2019.
The first player born in the 2010s to make a WTA final, she called her week in the 250-level event a "miracle journey" after her quarter-final win over sixth-seeded Caty McNally.
In her first WTA main draw match she advanced past top-seeded Ekaterina Alexandrova, who retired with heat illness with Liutova leading 7-6 (2), 4-6, 5-4.
She beat Australian Maya Joint in the second round before knocking off McNally 6-3, 6-4.
In Sunday's final she will face either 114th-ranked Czech Darja Vidmanova who beat Renata Zarazua of Mexico 6-3, 6-3 in the other semi-final.
Vidmanova, 23, will also be playing her first WTA final.