Worley is 13th in the World Cup standings and fifth in the giant slalom rankings.
For his second gold in the giant slalom in Sierra Nevada he made up 0.81 seconds on the first-leg leader to top the podium.
Finland's Tanja Poutianen finished fourth while Slovakia's Tina Maze -- who took gold in the Super-G and silver in the Giant Slalom -- finished fifth.
France are currently lying second with two golds -- Marion Rolland in the Downhill and Tessa Worley in the Giant Slalom -- one silver and one bronze.
Meanwhile, Austria's Marcel Hirscher increased his advantage in the battle for the men's overall World Cup title with second place in the giant slalom at Garmisch-Partenkirchen in Germany.
France's Grange tore ligaments in his right knee in the giant slalom at Beaver Creek, Colorado, last weekend, while Austria's Hosp was airlifted to hospital with a similar injury at the season-opening event at Soelden in October.
However, Canada's Kucera lost the chance to compete in his home Olympics when he broke his left leg after crashing in the super-giant slalom at Lake Louise in Alberta last month.
It was a good day for American skiers, with Ted Ligety triumphing in the men's giant slalom in Adelboden, Switzerland.
Shiffrin's victory is the U.S.'s fourth of the championships -- adding to Ted Ligety's wins in the Super-G, the Giant Slalom and the Super Combined -- and consolidates their place at the top of the medal's table with a total of four gold and one bronze.
Miller still intends to compete in the season's opening giant slalom in Soelden, Austria, on 23 October, and is now due to fly into Innsbruck on Thursday, several days later than originally planned.
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Maze also won the super-G gold at the recent world championships in Schladming in Austria and claimed two silvers in the super-combined and giant slalom.
Maze has already secured the overall and giant slalom titles and now leads in the slalom and the super-G disciplines.
It was Fenninger's second win of the season having won the giant slalom in Semmering, Austria, in December.
The full name for the race is the super giant slalom and it was first included in the 1988 Winter Olympics in Calgary.
Ligety will get a chance for a hat-trick of golds in Friday's giant slalom -- he won the title in 2011 in that discipline.
Ligety, who claimed the giant slalom title in Schladming, was only fifth going into the second leg and could not make up the deficit.
Ligety, who had won gold in the Super-G, super-combined and giant slalom, was the first man to achieve such a feat since Claude Killy in 1968.
The fact that she had done so well in the super-G, which was even less her discipline than the giant slalom, made me think that we were about to witness something pretty special.
The Austrian was beaten by Ted Ligety on Saturday when the American took advantage of his rival's mistake to win the giant slalom, but this time Hirscher recovered from eighth place in the opening run to beat compatriot Mario Matt and third-placed Italian Manfred Moelgg.
He was crowned 2003-4 champion on Saturday when a giant slalom at the World Cup finals in Sestrieres in Italy was cancelled because of fog.
But 2011 saw Ligety claim his first world title, winning the giant slalom at Garmisch and then going on to clinch his third World Cup crown in his favored discipline.
Nagano hosted the Winter Olympics in 1998 and a point of pride for Mr. Usui is that he skied a course used for the giant slalom.
MARIBOR, Slovenia (AP) Lindsey Vonn beat rival Tina Maze on the Slovenian's home snow and in her best discipline Saturday, earning a surprising victory in a giant slalom and her second win in a week.
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