Sunday after finishing third in the first run.
Kostelic scored his 28th career victory.
Austria's Marcel Hirscher was second and fellow Austrian Mario Matt was third.
Kostelic won in Kranjska Gora in 2003 as well and today's podium was his fourth there and the 58th in his career.
In the World Cup Men's standings, Kostelic is fourth in slalom points (475) and fifth in overall points (840).