The 22-year-old Vogt performed when it counted Tuesday at the Sochi Games, scoring 247.4 points on the normal hill at the Rus-Ski Gorki Jumping Center.
Daniela Iraschko-Stolz of Austria took silver and Coline Mattell of France earned bronze.
Sara Takanashi of Japan, the World Cup leader in the sport and heavy favorite heading into the Sochi Games, was a disappointing fourth.
Vogt, who has four second-place finishes in World Cup events this year, had been quiet in training runs, allowing Takanashi and Iraschko-Stolz to take much of the hype as they dueled for supremacy.
"I can't find the right words," Vogt said. "I'm just speechless because training yesterday was not so good. Now I've improved today. I've not won a World Cup till now. It's unbelievable."
Iraschko-Stolz said she had to battle some anxious moments before her silver medal-winning performance.
"It was difficult to jump today because of nerves, difficult to overcome it," Iraschko-Stolz said.
In 2011, the International Olympic Committee agreed to allow the women to compete at Sochi - 90 years after men did at the inaugural Winter Games in 1924.
The 17-year-old Takansashi set the tone early, jumping last in the warm-up and beating Iraschko-Stolz by a meter.
When Takanashi's placing lit up the scoreboard, a group of Japanse fans blew kazoo-like devices and waved a large flagpole containing a carp kite - a fish that the Japanese consider good luck, followed by the Japanese flag, and then a banner with Takanashi's picture on it.
The carp didn't bring her much luck.
Takanashi finished the first round in third place, meaning she would jump third-last in the final round, a place she was not used to considering she has led and won so many World Cups this year.
Iraschko-Stolz took the lead with three jumpers to go, leaving Vogt needing a good jump to overtake her. It wasn't as good as the Austrian's final jump, but enough to give the German a six-point edge.
Japan had been counting on Takanashi to end an Olympic gold medal drought. The country's last gold came at the 2006 Turin Games when Shizuka Arakawa won the ladies singles in figure skating.
"I couldn't jump the way I wanted to on both attempts." Takanashi said. "I came here wanting to do my best. I'm incredibly disappointed."
Sarah Hendrickson, the 19-year-old defending world champion from Park City, Utah, finished 21st of 30 starters, clearly still affected by right knee surgery she underwent in August. Although she showed improved form Tuesday, she plans to take the rest of the season off.
Hendrickson says she wasn't surprised to see Takanashi off the podium.
"It's a crazy world the Olympics," she said. "It shows she is a human being. I wish I could tell her she is still an amazing athlete and that she has many good years to come."
Hendrickson, because she has no ranking from being off the World Cup circuit with her injury, was the first jumper in the Olympic final.
"It's an amazing feeling to be the first one to jump in the first women's ski jumping competition at the Olympics," she said. "My performance was not the best, but I kind of expected it."
Two other Americans from Park City competed - Jessica Jerome was 10th and former world champion Lindsey Van 15th.
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