The Swiss skier had just defeated unacknowledged AJ Ginnis, who was just as pleased with his second place. Zenhaeusern finished 1.02 seconds ahead of Ginnis, who became the first skier from Greece on a World Cup podium.
Ginnis was 21st after the opening leg before posting the fastest time in the second.
"Really unbelievable, a dream," said Ginnis, whose career has been marred by knee injuries. "Last year, I tore my ACL again so I had to come back again. Everything went well today, I had luck and I skied well."
Ginnis, born in Greece and whose wife is American, was 12 when he moved to Austria with his father, a ski instructor. He went to the United States three years later and competed for the U.S. ski team at the 2017 worlds.
He was dropped from its program following several injuries and has been starting for Greece since 2018. His previous best result was 11th from a slalom in Austria two years ago.
The World Cup season contains two more slaloms after the World, which start Monday.