The success on the Austrian slopes in St Johann raised hopes for a successful world championship which takes place in three weeks at the American Deer Valley venue.
“This is an absolute dream and in front of this background too,” said Zacher, whose parents were there to see her win. “It was the perfect race and the perfect moment for the first world cup victory.”
Hedda Berntsen of Norway came second.
The 22-year-old came 17th in the last Olympics, where the sport was introduced to the Games. Ski-cross involves four racers competing directly against each other over a course which includes jumps, bumps and curves.
Funding for the German team has been more than doubled recently, to around €280,000, with an eye on the 2014 Olympics in Sotschi. The German ski team is hoping to collect five medals in freestyle, ski-cross and snowboarding, despite having come back from the last Olympics in Canada empty-handed.