The fired-up Goggia, who was also victorious in Austria's Bad Kleinkirchheim on Sunday, shone ahead of the Feb. 9-25 Winter Olympics in Pyeongchang, South Korea, the country where she celebrated her only two previous World Cup wins.
Foggia claimed the downhill in Jeongeson on March 4 last year and the next day's Super G, and next month's games could see more success for the 25-year-old from Bergamo.
Vonn, looking her for her 79th career World Cup win, came close to dislodging Goggia but an error in the lower part of the fast and treacherous course confined her to a second-place finish 0.47 seconds behind the Italian.
The versatile Shiffrin finished third, 0.84 seconds off the pace, in her maiden Cortina downhill and only her fifth start in the event, highlighting her potential to win medals in all five alpine skiing disciplines in Pyeongchang.
The upper half of the iconic course claimed early casualties as podium contenders Michelle Gisin and Federica Brignone missed the early gates and Christine Scheyer crashed out before Goggia produced a flawless run.
The race was the last in fellow American Julia Mancuso's illustrious career, and she glided down the piste to cheers from the crowd.
The 33-year-old Mancuso is the most decorated U.S. Olympic skier with four medals and her final run drew tears from Vonn, who will carry American hopes in Pyeongchang alongside Shiffrin.
(Writing by Zoran Milosavljevic; Editing by Andrew Roche)
