The American took risks in the final section of the Planai course to win in 1 minute, 23.96 seconds.
Gauthier De Tessieres of France was 0.20 back in second. Aksel Lund Svindal of Norway, who won three of the four World Cup super-Gs this season, was another 0.02 back in third.
Defending champion Christof Innerhofer of Italy finished 1.09 off the pace.
"Today was unbelievable," said Ligety, who was the 10th starter. "It was a nerve-wracking 30 minutes, waiting for all the favourites to come down. (To) finally see (Svindal) come down right behind me was a huge weight off my shoulders."
Calgary's Jan Hudec was the top Canadian, finishing 1.56 back in 12th place.
"At world championships, it’s pointless to show up unless you want to win," said Hudec, who started 14th and clocked a time of 1:25.52 seconds. "Top three places count here — everything else is forgotten pretty quickly.
"I’m a little bit frustrated because I’m not 100 per cent sure where the time went. I had a good run but it wasn’t good enough."
Ligety made a super-G podium only once before, finishing second in a World Cup at Val d'Isere, France, in 2009. This season, he had finished fourth in two races.
"I am having a good year in super-G but I didn't think this was possible," Ligety said. "I thought I had a chance for a medal. I knew I had to take many risks at the bottom to have a chance. I tried not to slide and to ski as clean as possible."
The gold is his second medal from a world championship. Two years ago, he won the giant slalom in Garmisch-Partenkirchen, Germany.
It was the second medal in two days for the U.S. ski team, one day after Julia Mancuso took third in the women's super-G.
"Julia always does well at the big events," Ligety said. "I knew I had a good chance myself today and it's great to make a contribution to the success of the team."
Lindsey Vonn crashed in Tuesday's race, tearing knee ligaments that will keep her out for the rest of the season.
"It's very sad for Lindsey because she was doing great but it didn't matter for my race," Ligety said. "You have to move on. I am sure she will be back next year. As a ski racer, you can't let that affect you too much."
Ligety trailed then-leader De Tessieres by 0.41 at the first intermediate time 30 seconds into his run. He reduced the deficit to 0.06 over the next 30 seconds and beat the Frenchman in the bottom section.
De Tessieres, whose best super-G result on the circuit was eighth, had not qualified for the French team but replaced Johan Clarey, who pulled out with a back injury on Sunday.
"It's difficult to describe this week," De Tessieres said. "I hadn't qualified and got a phone call from the coach a couple of days ago and now I am here. I am so happy. It's amazing, a crazy story."
Several favourites led Ligety at the first split, including Austria's Matthias Mayer, Italy's Matteo Marsaglia and Innerhofer, and Svindal.
The course was set by Norway coach Tron Moger, who also placed the gates when Svindal won the super-G in Val Gardena, Italy, in December.
"It was tough," Svindal said. "I took a lot of risks and had a small mistake at the end. The conditions were OK, but not ideal. With this (low) light, you don't see the bumps. I am satisfied. Ted did just great. He would have had a great run with number 22 as well."
Manuel Osborne-Paradis of Vancouver was 16th while Benjamin Thomsen of Invermere, B.C., was 19th and Erik Guay of Mont-Tremblant, Que., was 23rd.
— With files from The Canadian Press