Slovenia's Tina Maze took her second silver of the Games while Austria's Elisabeth Goergl, the overnight leader, had to settle for her second bronze.
Austria's men and women have dominated on the slopes over the years but the giant slalom has eluded the women since the race was first introduced at the Games in 1952.
With three in the top four after Wednesday's first run, the Austrians had looked set to end that wait but Rebensburg, lurking in sixth place, had other plans.
"It sounds so strange, it's unbelievable," said Rebensburg, who has yet to win on the World Cup circuit, when asked how it felt to be an Olympic champion. "I think it's going to take a few days for me to realise it."
Germany's last female winner in the discipline was Ossi Reichert at the 1956 Cortina d'Ampezzo Games in Italy. The country's women have now won two of the four races to date, with Maria Riesch triumphant in super combined.
Maze added a silver to the one she took in super-G. "It's great. When I arrived here of course I knew I was a strong racer and could race well but I didn't expect I would take two silvers," she said.
Goergl said the second leg, with cloudy conditions on the upper stretch, was softer than she had expected: "I tried everything, it was a big fight," she said.
The race was strung out over two days, a departure from the usual format, due to mountain fog preventing organisers from holding the second run after the first on Wednesday.
American Lindsey Vonn went out in Wednesday's first leg in a crash that also scuppered the chances of team mate Julia Mancuso, the 2006 champion and a double silver medallist at these Games.
Eighteenth after the first leg, she rescued some pride with eighth place overall.
"I'm happy and proud for the girls on the podium," she said.
"I was pretty close but I guess I'll wait for another four years.
"Yesterday was so emotional," added the skier, who fled the finish in tears after the first run but was smiling again a day later. "It was really tough and I dealt with it.
"It sucks, but sometimes that's what happens in life."
Britain's Chemmy Alcott finished 27th, 2.83 seconds behind Rebensburg.
"I felt like I really knocked the door down. I didn't really make a mistake, I just skied too hard,” she said. “I'm disappointed because it just didn't happen today.
"It was a bit of a bad day at the office. Everybody has them, but you just don’t want it at the Olympics."
