Overall World Cup leader Marcel Hirscher of Austria finished fourth, 0.94 behind.
Ligety’s first gold came in combined at the 2006 Turin Games as a 21-year-old — before he had ever won a World Cup race.
The only other American to win two Olympic golds in Alpine skiing was Andrea Mead Lawrence, who took both the women’s slalom and giant slalom at the 1952 Oslo Games.
Four other American men — Bode Miller, Phil Mahre, Tommy Moe and Bill Johnson — have won one Olympic gold.
Ligety had such a large lead after the opening run — 0.93 seconds — that he could afford to ease up a bit on his second trip down, when he was only 14th fastest. But that was more than enough to give the U.S. its first gold in Alpine skiing of the Sochi Games.
Ligety celebrated by swirling around in the finish area while still on his skis then raised his arms while sitting down on the snow. The crowd realized he had won even before he crossed the line, and showered him with applause for the last few gates.
Conditions were perfect, with the temperature hovering near the freezing level and skies partly cloudy.
In both runs, Ligety showed off his unparalleled technique of arcing turns, leaning down and touching the snow with his hips, gloves and thighs at every opportunity to get the best angles. Other skiers displayed sharper turns but Ligety’s were far more fluid.
“Ted goes so round that his turn is naturally a longer radius,” said Miller, who finished 20th in what he said was his final race in Sochi. “He generates more speed and links one turn to the next and because he has so much space, he never pinches or gets in trouble because he’s always way far from the gate.”
Ligety has been the best giant slalom skier for several years, although after failing to win a medal at the 2010 Vancouver Games, this was his crowning achievement.
Ligety won nine of 14 World Cup giant slalom races this season and last season. He took gold in GS at the last two world championships and won the season-long World Cup title in the discipline four of the last six years.
“I think he’s one of the best GS skiers in history,” Miller said. “He’s so much better at it than everybody else. ... He just is so consistent. He makes no errors.”
At last year’s worlds in Schladming, Austria, Ligety also won gold in super-G and super-combined, making him the first man with at least three golds at a worlds since Jean Claude Killy earned four back in 1968.