Ligety clinched his 15th top spot in the discipline in a combined time of two minutes 28.67 seconds.
The world champion owed his fourth win of the winter to World Cup holder Hirscher.
Austrian Hirscher, who had been on the podium of the last nine giant slaloms he entered, was leading Ligety by more than a second when he missed a gate close to the finish line and had to settle for 16th place.
Ligety beat Germans Fritz Dopfer, 1.15 seconds adrift, and in-form Felix Neureuther, who finished 0.09 behind his team-mate.
With 15 giant slalom wins, Ligety became the third most successful skier in the discipline, level with Italy's Alberto Tomba and behind Swede Ingemar Stenmark and Swiss Michael von Gruenigen.
"I absolutely wanted to win this because it was a real chance to seize," said Hirscher after he was to explain why he did not ski more conservatively.
"Today I stretched my limits but it's good to see you can beat Ligety. I took too many risks and I paid the full price."
Ligety's victory was well deserved.
"I really went after this one. It took so long it's a real relief. Okay, it was handed to me by Marcel but I'm not going to refuse it," he said.
"Marcel should have won this but the same thing happened to me here a couple of years ago when I lost after a silly mistake close to the finish.
"It's a shame but that's skiing. I'm really proud of this for it was the only classic I had yet to win.".
Ligety had never been able to even reach the podium on the Swiss giant slalom course, lined as usual by some 40,000 fans.
While Ligety made a giant step towards claiming back the discipline's crystal globe in this last giant slalom before the world championships in Schladming next month, Hirscher lost precious points in the race for the big globe.
His closest rival Aksel Lund Svindal made it clear he was far from giving up with a good sixth place, 1.86 behind Ligety, yet he was disappointed after winning on the same slope two years ago.
"After being fourth in the morning run, I was expecting better than a sixth place. I can't win giant slaloms like I used to but I really look for a podium," he said.
The Norwegian is only 26 points behind Hirscher in the overall standings, making Sunday's slalom on the same piste another key race for the Austrian, who will have the double pressure of defending his crown and collecting vital points.
- Sports & Recreation