Vonn tore ligaments in her right knee and broke a bone in her lower leg when she lost balance while landing after a jump. She was taken to a hospital by helicopter.
Maze attacked all the way, winning in 1 minute, 35.39 seconds and beating Lara Gut of Switzerland by 0.38. Julia Mancuso of the U.S. was third, 0.52 behind.
"The gold medal means a lot to me," said Maze, who is having a standout season in the World Cup and is quickly closing in on the overall title. "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 and was called off after 36 racers because new clouds of fog were moving in. The results stand, with the top-30 racers having started their run.
"I was prepared for a long day," said Maze, who now has four world championship medals. "World championships are special, you have to stay focused. I knew we would race today despite all the delays."
Days of snow and rain softened the course, especially in the lower part. The evening before the race, Atle Skaardal, the women's race director for the international federation, called it an "extreme situation." The fog further complicated matters.
The clouds caused poor visibility in the middle section, the steepest part of the 1.4-mile Streicher course where skiers race at up to 62 mph.
Organizers repeatedly delayed the start. Clouds finally moved after three hours. Despite light snowfall and rain setting in, the race began.
Several racers struggled with the changing conditions, with favorites like Maria Hoefl-Riesch of Germany and Anna Fenninger of Austria missing gates and failing to finish, and Viktoria Rebensburg of Germany coming 0.94 off the leading time in eighth.
"It was OK," Maze replied when asked whether the race should have been started. "World championship races often have special conditions. The mistakes from the girls were not because of the slope."
Mancuso wasn't fully satisfied with the run that earned her a fifth world championship medal, two years after winning silver in super-G in Garmisch-Partenkirchen, Germany.
"It's always really nice to win a medal but of course I know I could have a better run," the American said. "It was not a perfect run. My brain shut off halfway down the course so that's why I had some mistakes but I knew I was going fast. This was the kind of course on which you have to be on the limit."
Mancuso said it was "really hard" to race after Vonn, who started three racers earlier.
"I didn't see it on TV," said Mancuso, who was in the start gate preparing for her run when the crash happened.
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. The four-time overall World Cup champion received medical treatment on the slope for 12 minutes before being taken to the hospital. She left for the team hotel later Tuesday.
Vonn trailed Maze by 0.12 seconds shortly before the crash. The race continued after another 15-minute delay.
Gut had two mistakes in the turning middle part that slowed her 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, where she became the youngest Swiss skier to medal at 18.
"It's fantastic to come second," Gut said. "My run was poor, I was too late at many turns and was surprised with my time."
After eight starters, the race was interrupted for 15 minutes following a crash by a course worker, who was removed by helicopter. He was brought to the hospital with a broken nose.
The men's super-G is scheduled for Wednesday and could also be affected by the weather, with overnight snowfall forecast.