Goggia beat Germany's Emma Aicher by 0.24 seconds to go 84 points clear of New Zealand's Alice Robinson, who could manage only seventh.
Norway's Kajsa Vickhoff Lie completed the podium in Soldeu, with Switzerland's Corinne Suter fourth.
Italy's Federica Brignone, the Olympic champion and a double gold medallist at the Milano Cortina Games after breaking her leg last April, returned to action and was eighth.
Aicher is third in the race for the super-G crystal globe, 116 points behind Goggia, with two rounds remaining worth a total of 200 points.
The win was Goggia's second of the season in super-G.
A men's super-G in the German resort of Garmisch-Partenkirchen was cancelled due to fog.