The 25-year-old, hot favourite for the gold medal at Sochi 2014, produced a track record in her first run in front of a home crowd and it was too much for her rivals.
Canadian Alex Gough finished in second place while her teammate Kimberly McRae achieved her first career World Cup podium finish in claiming third.
Geisenberger holds the top position in the overall rankings with a total of 785 points, followed by her teammate Tatjana Huefner on 551 point and Gough third on 541 points.
"From start to finish my first run was really good," said Geisenberger, who will skip the final World Cup round to prepare for Sochi.
"They all tell me that I'm the top favourite to win the gold medal at the Games. However, my aim is to claim a medal. The pressure is high enough and I don't need to put myself under even more pressure."