Kostelic beat French Julien Lizeroux in the final round. In the previous rounds in this event he defeated Kjetil Jansrud of Norway, Austrian Reinfried Herbst in a quarter-final and German Felix Neureuther in a semi-final round.
In the parallel slalom race for women, Maria Pietilae-Holmner of Sweden was the winner.
The next World Cup slalom races are to be held on Mount Sljeme overlooking Zagreb: women will compete on Tuesday and men on Thursday.