The American timed 1 minute, 23.96 seconds on the Planai course to beat Gauthier De Tessieres of France by 0.20.
Aksel Lund Svindal of Norway finished third, 0.02 back. Defending champion Christof Innerhofer of Italy finished 1.09 off the lead.
It was Ligety's first victory in the discipline. He finished second in a World Cup super-G in Val d'Isere, France, in 2009. This season, he has finished fourth in two races.
Ligety won the giant slalom at the world championships two years ago in Garmisch-Partenkirchen, Germany.
The results were provisional as some lower-ranked skiers in the 82-man field were still to start.
Press; By ERIC WILLEMSEN]
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