Rebensburg, who had never won a major race, won in a two-run combined time of 2 minutes, 27.11 seconds.
Tina Maze of Slovenia was second, 0.12 seconds behind, matching her result in super-G, and first-run leader Elisabeth Goergl of Austria added another bronze, 0.49 back, duplicating her downhill finish.
Defending champion Julia Mancuso of the United States finished eighth.
The first run of the race was held Wednesday, but dense fog forced organizers to postpone the second leg for a day.
There was more fog Thursday, and it got worse just after Rebensburg's run.
The 20-year-old Rebensburg stood only sixth after the opening leg. Her best previous result was second in the last World Cup GS before the Vancouver Games in Cortina d'Ampezzo, Italy. Before that, she had never finished on the podium.
Rebensburg has been threatening to break out for several seasons. She finished eighth in giant slalom at the 2007 world championships in Are, Sweden, when she was just 17; then was ninth at last year's worlds in Val d'Isere, France.
Rebensburg's coach, Christian Schwaiger, set the opening run.
Like the first leg Wednesday, organizers again rushed to get the race in, sending down racers at 60- and 75-second intervals - meaning there were often two skiers on the course at a time - and abandoning TV breaks before the first 30 racers came down and the medals were decided.
The short intervals created problems in the first leg, with Mancuso's first trip down interrupted because teammate Lindsey Vonn crashed out immediately before her - breaking her right little finger.
Mancuso had to be brought back up for another try and eventually placed 18th in the opening leg. The Californian had the third-fastest second run to move up 10 spots in the final standings.
The race was briefly interrupted after 18 skiers came down due to an apparent timing equipment problem.
Only one more women's race remains on the Alpine schedule, Friday's slalom.
Maze has had a stellar games, also finishing fifth in super-combined.
“It's great. I didn't expect that I would take two medals,” Maze said. “I was never racing so good at the big events, but this time it's different, and I skied confident.” Goergl's medal haul now matches that of her mother, Traudl Hecher, who also won two Olympic bronze medals - in downhill at the 1960 Squaw Valley Games and 1964 Innsbruck Games.
Goergl also won a bronze in super-combined at last season's worlds, and she was already claiming family bragging rights.
“With my world championships medal it's five,” said Goergl, whose older brother Stephan is also a World Cup skier.
Goergl said the overnight wait didn't affect her.
“I had the same focus as if we had started the race today,” she said. “I wanted gold today.”
