Kostelic won with a combined time of two minutes 53.70 seconds from Sweden's Anja Paerson. Austria's Marlies Schild was third.
The 23-year-old Kostelic managed to defend the title. She has now won three gold medals in combined following her success in the Olympics at Salt Lake City and the world championships at St Moritz two years ago.
Croatian television said Kostelic was the first in the world to have won both the downhill and the slalom race in a combination race.