Iraschko-Stolz had landed a monster second leap of 104.5 metres, the longest of the night, to move up from fifth place.
Vogt could only manage 97.5 metres with her second jump and faced an agonising wait before learning she had won by less than a point. She promptly collapsed to the snow in floods of tears and had to be supported by her team mates.
"The first seconds were terrible for me. It took such a long time for the result to come up," she told a news conference.
"I am a still a bit astonished that I could cope with the pressure," said the 22-year-old world number two, whose win marked the end of a 13-year fight by female athletes to take part in the Games.
Vogt finished with 247.4 points, just ahead of Iraschko-Stolz on 246.2. In a major surprise, French teenager Coline Mattel took the bronze, relegating world number one Sara Takanashi of Japan to fourth place.
Iraschko-Stolz, who played a major part in the campaign to have women jumpers included in the Games, said the result was worth a gold medal to her.
"I lost the gold in the first round. In the second I went fully on the attack and that was really cool. But silver is great," the 30-year-old told Austrian television.
Mattel told reporters that she was very grateful to the Austrian for all she had done for the sport.
"She definitely deserves to be on the podium. It's important that she is on the podium. She fought for it," she told reporters.
Women had pressed the International Olympic Committee since 1998 to be allowed to jump, going to court to challenge their exclusion from the 2010 Vancouver Games, but were repeatedly rejected on the grounds there were not enough good female jumpers.
The IOC announced in 2011 that women could take part in Sochi, but only on the normal hill, and limited the number of competitors to 30. In the men's jumps, 50 take part.
Women are also not allowed yet to jump the large hill or take part in the team event.
Women had long insisted they were as good as the men and Iraschko-Stolz's second jump seemed to support this argument. When Poland's Kamil Stoch won the men's normal hill title on Sunday, his longest jump was 105.5 metres.
The result was a big disappointment for Takanashi, the 17-year-old runaway World Cup leader who never looked like living up to her position as favourite.
"What I feel is not pressure. But I feel the expectation from a lot of people," she told reporters, saying she planned to compete in the next Winter Games.
World Champion Sarah Hendrickson of the United States, who made the Games despite suffering a bad knee injury last year, looked tentative and put in two mediocre efforts to end in 21st place.
Deedee Corradini, the president of Women's Ski Jumping USA, said the occasion was so important that it did not matter who ended up with the gold.
"Whoever wins, we are all going to be thrilled," she said before the competition started.