Vogt, who led after the first run, grabbed a total 247.4 points with jumps of 103 and 97.5 metres, and sank to her knees in tears after seeing the results. 2011 world champion Daniela Iraschko-Stolz of Austria claimed silver with 246.2 points, ahead of third-placed France's Coline Mattel on 245.2 points.
For Vogt, who has made eight World Cup podiums this season but arrived in Sochi still chasing her first win, her victory came as a genuine surprise. “I cannot find the right words,” she said. “I wouldn't have thought it was possible three hours ago. “It's amazing, I'm the first women’s Olympic champion in ski jumping. I've not won a World Cup till now. It's unbelievable.”
But the biggest surprise was the absence from the podium of Japanese teen sensation Takanashi, currently World Cup leader and reigning Youth Olympic champion.
The 17-year-old was the firm favourite to win gold on the RusSki Gorki hill, having won 10 out of 13 World Cup races this season, but only managed a third place after her first jump.
A second jump of 98.5 metres was not enough to catch up with her rivals and she finished fourth.
“I couldn't jump the way I wanted to on both attempts,” said the three-time junior world champion and World Cup title winner from last year. “I came here wanting to do my best. I'm incredibly disappointed.”
But despite that disappointment, she managed to recognise the positives too: “It's a good experience being at the Olympic Games and I'm glad to be part of it.”
Tuesday's floodlit event had been widely expected to be a battle between Takanashi and Iraschko-Stolz, her senior by 13 years.
The Austrian stood in fifth after the first jump but put in a risky performance in the final round, reaching a whopping 104.5 metres and holding her landing despite coming close to a fall.
“It was a very good feeling, my best jump today," she said.
“I was a little bit shocked because I jumped so far and my landing was not very good, but I think I lost the gold in my first jump and now I have silver.”
Mattel, 18, who already won a World Cup race in Sochi back in 2012, was also left struggling for words.
“It's just amazing. It might be the best day of my life so far. I was very stressed,” said the French athlete. “Yet somehow I'm glad it's over. It's been the longest day of my life and I did it.”