Sakkari won his hard-fought ticket against Romanian Irina Begu (56th) 6-4, 6-7 (4/7), 6-4 in 3:04.
On the other hand, it only took 1h11 for Kontaveit to dismiss Ostapenko (25th) 6-3, 6-4, who however played the second set with a strapped ankle.
"I don't even know how I managed to win this match. But here I am very happy," Sakkari savored after qualifying.
In what will be his fourth final on the WTA circuit at 26, Sakkari will seek the second title of his career.
Sakkari is one of the revelations of the year 2021 which saw her go from 20th to 6th in the world thanks in particular to two Grand Slam semi-finals, at Roland-Garros and at the US Open.
Facing Kontaveit on Sunday, the Greek will have a tough opponent who has just had a 19th indoor success in a row, winning against Ostapenko, victorious at Roland-Garros in 2017.
"In front of her (Jelena Ostapenko) we had to play aggressive tennis and wait for my chance. And I played exactly like that... I will have a very difficult final tomorrow against Maria (Sakkari) but I hope that It's going to be fine...", Kontaveit said after his half.
The Latvian will try to afford the sixth title of her career, after a prosperous year 2021 with 4 tournaments won.
© 2022 AFP