Kontaveit faced No.2 seed Kvitova having previously toppled Paula Badosa and Belinda Bencic in straight sets.
Her last-four victory was even more comprehensive, as Kvitova went down 6-0 6-4 in 71 minutes.
Kontaveit advances to her fourth final of 2021 and avoids facing Iga Swiatek, who defeated her at the US Open – her only loss since winning the Tennis in the Land title last month.
But the Estonian must take on the woman who knocked her out of the Tokyo 2020 Olympic Games in Maria Sakkari.
No.4 seed Sakkari took down No.1 seed Swiatek 6-4 7-5 to make her first WTA Tour final since 2019.
Sakkari had lost nine consecutive semi-finals since then, while Swiatek had never lost at this stage of a tour-level event, but the Greek was a deserving victor.