Eastbourne champion Kasatkina, who has lost four finals this year, breezed through the opening set in double quick time as Andreeva looked nervous.
After winning the opening game of the next set, Kasatkina faltered and her close friend Andreeva rallied to draw level when the world number 11 sent a backhand wide.
Andreeva built a 3-0 lead in the decider but the momentum swung Kasatkina's way again as the youngster's unforced error count climbed rapidly.
Kasatkina clawed her way back to secure the eighth trophy of her career and she will return to the world's top 10 on Monday.
"In the first set I gave everything, I was super focused and the level was so high," Kasatkina told reporters.
"But obviously after that, I dropped a little bit and Mirra was there ready to take it over. She's this kind of player who never gives up and to win any point you have to almost die on court.
"I feel like I did a miracle in the third set because it was a very tough moment. I was not very far from losing belief... In tennis, the top 10 is a very important achievement."
Andreeva was in tears after missing a golden chance to her claim a second title this year after her triumph in Iasi, Romania.
"I saw you crying a lot, it's okay, you're gonna have a lot more finals," Kasatkina told Andreeva after the match.
"I hope we can share some of them."