A race that came down to a few hundredths of a second saw Hirscher finish fourth, giving him enough points to clinch the sport's biggest prize.
Ligety won the race and thereby tied the Austrian on points in the season-long discipline standings, giving the American the GS title on a tiebreaker as he had more race victories.
"It's an unbelievable happy day," said Hirscher, content to concede the discipline to the American dubbed "Mr. GS" by race announcers.
"My big goal was the overall World Cup title and I got it and I'm so happy," said the 25-year-old Hirscher, the first man to win three in a row since American Phil Mahre completed the feat in 1983.
Hirscher needed 19 points to overtake Aksel Lund Svindal of Norway, who led the standings going into the race but skied out in the first run. Fourth place gave the Austrian 50 points.
Hirscher completed Austria's first overall title double since 2002, after Anna Fenninger clinched her first women's title this week. They both come from villages near Salzburg and raced each other as juniors.
Ligety earned his victory in a crowd-pleasing race by just 0.03 seconds ahead of runner-up Alexis Pinturault of France, in a two-run combined time of 2 minutes, 15.
"I'm super-thrilled. That was by the skin of my teeth today," Ligety said.
He still relied on a big assist from first-run leader Felix Neureuther of Germany to make clinch the discipline title as the narrow margins all fell Ligety's way.
Ligety, the Olympic champion in GS, was second-fastest in the morning and had time in the start house to absorb the second-leg target set by Hirscher.
Hirscher finished outside provisional leader Pinturault's time, leaving Ligety an opening.
The 29-year-old American came down barely faster than Pinturault, drawing applause from Hirscher who was in the finish area already knowing he was overall champion.
Ligety then needed his good friend Neureuther to finish second or third in the narrow time gap between himself and Hirscher.
Neureuther did it in the tightest way possible, finishing 0.01 ahead of Hirscher, who was relegated to fourth. With 10 fewer points awarded for fourth than third, he fell into a tie with Ligety on 560 over the eight-race season.
Ligety got the tiebreaker with five World Cup race wins against Hirscher's two.
"Felix, I owe a lot of beers," Ligety said.
Hirscher was smiling later, after watching Ligety and Neureuther roll around the finish-area snow in celebration.
"He is not allowed to travel to Austria. It is over. Just kidding," Hirscher said of Neureuther's intervention.
They will renew their rivalry Sunday for the season-long slalom title.
"He is very mad about me so it's going to be very close," said Neureuther, who leads Hirscher by five points in the slalom standings. Henrik Kristoffersen of Norway is also in contention.
Svindal faded again, extending his disappointing series of results since leaving the Sochi Olympics early, affected by allergies and without a medal. He is not competing in Sunday's slalom.
"It was a good season but it could have been fantastic," said Svindal, who won the World Cup titles in downhill and super-G though all but conceded the overall title to Hirscher earlier in the week.
"That was too bad, because I had a really good opportunity to win the biggest thing a ski racer can win," said Svindal, a two-time former overall champion.
Ligety completed a race double for the U.S. team Saturday, with Mikaela Shiffrin earlier winning her fifth World Cup slalom this season.
The American anthem played four times in quick succession for a crowd of 10,500 at the Swiss venue—twice each for Ligety and Shiffrin's race and season title victories.
The Austrian anthem will dominate Sunday, when Hirscher and Fenninger get their giant crystal globes.