Zanevska twice found herself trailing 3-0 in the battle between two first-time WTA singles finalists, but rallied to win 6-4 7-6 (7-4) on the clay in Gydnia on Sunday.
World number 165 Zanevska had never played in a quarter-final on the main tour before making the last four in Lausanne last week and the in-form Belgian now has a first title to her name.
The 27-year-old was granted a special-exempt entry into the Gdynia main draw due to her run in Switzerland and is now projected to re-enter the top 120 in the rankings.
Kucova was left to reflect on what might have been, having started both sets so strongly before failing to press home her advantage in a topsy-turvy championship match.
The Czech, ranked 150th, saved four match points before forcing a tie-break but was beaten in an hour and 51 minutes.