Ligety turned in a combined two-run time of 2 minutes, 14.76 seconds, edging the Austrian, who finished with a 2:15.13 and had earlier clinched the overall World Cup points title.
Alexis Pinturault of France took third.
The win Saturday was Ligety's sixth first place in eight World Cup giant slaloms this season.
He led after the first run and had the second-fastest time in the second run.
"It was a really cool season and to finish it up with a victory ... I couldn't be more pleased," said Ligety, the first World Cup skier since Ingemar Stenmark to win six giant slaloms in a single season.