Vogt took the lead after the first round of jumping and held on for a narrow victory that served as yet another milestone at the Winter Games.
After years of lobbying by the athletes, women's ski jumping was finally added to the Olympic program for Sochi and American Sarah Hendrickson had the honor of performing the first jump of the competition when qualifying got under way.
Hendrickson eventually finished 21st.
Vogt has had four runner-up finishes on this year's World Cup circuit, but she had yet to win a competition until she captured the biggest prize of all.
She turned in a jump of 103 meters in the first round and when the judges points were added she had a score of 126.8. That gave her the lead over Coline Mattel of France, with current world champion Daniela Iraschko-Stolz of Austria back in fifth place.
Iraschko-Stolz then got off a jump of 104.5 meters in the second round and she vaulted into the top spot with only Vogt left to go.
Vogt jumped just 97.5 meters, but she earned four more points from the judges than did the Austrian competitor. When everything was added together Vogt had a combined score of 247.4 for the two jumps while Iraschko-Stolz had 246.2.
Mattel slipped back to third place and won the bronze with a score of 245.2. The top American in the inaugural event was Jessica Jerome, who wound up 10th.