Hirscher, the overall World Cup men's points leader, was in first place after the opening run Saturday but went down near the end of his second tour of the course, opening the door for Ligety to claim the victory with a combined run time of 2 minutes, 28.67 seconds.
"This has been a tough course for me in my career so I'm happy to get the win," said Ligety. "The second run was so dark and this hill is so tiring. I was lucky to have a little bit of reserve strength."
Fritz Dopfer took second and Felix Neureuther finished third. Aksel Lund Svindal of Norway was sixth.
Ligety was in third place in the overall standings, 103 points behind Hirscher, after Saturday's win. Svindal was in second place.