Kostelic covered the bumpy course in a combined two-run time of 1 minute, 45.81 seconds, finishing ahead of Marcel Hirscher who clinched the season slalom title with a second place.
"It's a wonderful feeling as it's not easy to stay at a high level in any sport nowadays and slalom is a particularly tough discipline where competition is really dense," said Kostelic.
Alexis Pinturault of France led after the first run, but skied out in the second run, opening the door for Kostelic to move up from third place.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys