Unics looked as though they would have to settle for Eurocup action when they slipped 19 points behind ASVEL Lyon Villeurbanne in the final qualifying match.
However, James White and D'Or Fischer starred as that deficit was wiped out with time to spare, Unics ultimately prevailing 88-79 at Ostend's Sleuyter Arena.
White scored 21 points, while Fischer contributed 18 plus eight rebounds to lead an improbable turnaround.
Unics will now compete in Group A of Euroleague, with Real Madrid among their opponents.
Veteran center David Andersen was unlucky to finish on the losing side after helping himself to 27 points for Lyon.