The 26-year-old Estonian, with six career titles to her name, will face former French Open champion Iga Swiatek of Poland who defeated Greece's Maria Sakkari, 6-4, 6-3, in Saturday's final.
She needed just 68 minutes to defeat last week's Dubai champion Ostapenko.
Kontaveit has been on a red-hot streak on the tour with five of her titles coming since last summer, the most recent of which was in St. Petersburg two weeks ago.
Seventh seed Swiatek will be chasing her fourth title after beating Sakkari for the first time in four meetings on the back of 20 winners on Friday.
The pair's first three meetings all came last year with Sakkari winning in straight sets. One of those clashes saw Sakkari end Swiatek's reign as French Open champion in the quarter-finals.