The Croatian slalom specialist trailed first-run leader Beat Feuz by almost three seconds in downhill, but edged the young Swiss skier for victory by 0.20 seconds. Kostelic, who also won this event last year, had a combined two-run time of two minutes 42.16 seconds.
Bode Miller of the United States was third, trailing Kostelic by 0.45 after finishing second-fastest in the downhill.
The 34-year-old Miller won this event in 2010.
Kostelic's 21st career World Cup win closed the gap on Marcel Hirscher of Austria in the overall standings. Hirscher did not enter Friday's race, and is scheduled to compete next in Sunday's slalom.
With the 100 World Cup points for victory, Kostelic — the defending overall champion — trails Hirscher by 130.
Kostelic also made a winning start to the defence of his seasonlong title in super-combined. He will likely be a strong favourite to win the classic combined event next weekend at Kitzbuehel, Austria.
Ted Ligety of the United States climbed to third overall, 232 behind Hirscher, after placing sixth Friday.
"It would have been easy to be seven-tenths faster in slalom," Ligety said. "I skied well at the top but was too conservative down the pitch."
Feuz rose to fifth in the overall points race, and Miller retained his sixth spot.
Miller's performance on the shortened downhill course suggests he will be difficult to beat in the classic Lauberhorn downhill on Saturday.
In the downhill portion of the super-combined, Ryan Semple of Whistler, B.C., crashed out on a section known as the Minschkante, where Olympic downhill champion Didier Defago of Switzerland went out in Thursday's training run. Semple was reported to be uninjured.
Louis-Pierre Helie of Berthierville, Que., also did not finish.Suggest a correction