Another Frenchman, Thoma Fanara, finished third behind Ligety, who turned in a combined time of 2 minutes, 31.99 seconds on the course at Alta Badia.
"This is the best GS hill on the World Cup circuit and to win today is super special, especially with three in a row," said Ligety, whose previous victories came in France and Colorado.
Ligety was able to hold off Richard in part because the Frenchman ran into trouble on the lower portion of the icy course. Richard still managed to turn in a career-best time of 2:32.13.
Didier Cuche of Switzerland placed fourth and Bode Miller of the United States finished 15th.
Celebrity Families of 2014 [PHOTOS]