Zanevska was twice behind in the fight between two first-time WTA individual finalists 3-0, but won 6: 4, 7: 6 (7: 4) on Sunday in Gydnia.
The number 165 of the world rankings Zanevska had never played in the quarter-finals on the main tour before reaching the last four in Lausanne last week, and the formidable Belgian now has a first title on her name.
The 27-year-old received due to her run in Switzerland had a special free participation in the main draw of Gdynia and is now expected to be included in the top 120 of the rankings again.
Kucova had to think about what could have been after she had started both sets so strongly before taking her lead in could not play an upside-down championship game.
The Czech in 150th place saved four match points before forcing a tie-break, but was beaten in one hour and 51 minutes.