Vonn lost her balance while landing after a jump and was taken to a hospital by helicopter with an apparent right knee injury. The four-time overall World Cup champion received medical treatment on the slope for 12 minutes before being airlifted to the hospital.
There was no immediate update on her condition.
Maze won the race in all-attacking style in 1 minute, 35.39 seconds, beating Lara Gut of Switzerland by 0.38. Julia Mancuso of the United States was 0.52 behind in third.
"The gold medal means a lot to me," Maze said. "I had a great run. Slovenia is a small country and has so many great athletes. That makes me really happy."
The race had been delayed by 3 1/2 hours because of thick fog hanging over the course, and was called off after 36 racers because new clouds of fog were moving in. The results stand as the top-30 racers had started their run.
"I was prepared for a long day," said Maze, who earned her fourth world championship medal. "World championships are special, you have to stay focused. I knew we would race today despite all the delays."
Gut had two mistakes in the turning middle part that slowed her down but attacked the bottom part for a strong finish to earn her third world championship medal all in silver. She took second in downhill and super-combined at the 2009 event in Val d'Isere, France, when she became the youngest Swiss skier to medal at 18.
Mancuso also wasn't fully satisfied with her run.
"It's always really nice to win a medal, but of course I know I could have a better run," the American said, adding it was "really hard" to race after the crash of Vonn, who started three racers ahead.
Vonn fell after a long jump, her ski came off immediately, and she slid off course and hit a gate before coming to a halt.
Vonn trailed Maze by 0.12 seconds shortly before the crash. The race continued after another 15-minute delay.
Days of snow and rain had affected the course and softened the surface especially in the lower part. The evening before the race, FIS women's race director Atle Skaardal called it an "extreme situation."
Several racers struggled with the conditions, with favorites like Maria Hoefl-Riesch of Germany and Anna Fenninger of Austria failing to finish.
"It's not a very difficult course, but in some parts you couldn't see anything," Fabienne Suter of Switzerland said.
After eight starters, the race was interrupted for 15 minutes following a crash by a course worker, who needed to be taken off the course by helicopter. There was no immediate information available on his condition.
The men's super-G is scheduled for Wednesday.