Stuhec, 26, claimed her first medal from a world championships or Olympics, with a faultless run down the icy course at speeds topping out at 125 km per hour.
Austria's Stephanie Venier took the silver medal, 0.40 seconds slower, with 2010 Olympic downhill champion Vonn 0.45 seconds off the Slovenia's pace.
Stuhec, whose ski technician is her mother Darja, emulated the feat of compatriot and Olympic champion Tina Maze who won downhill gold at the last world championships in Beaver Creek.
"I felt pretty good coming into the finish, not perfect but good enough," she said.
The 32-year-old Vonn, in the middle of another comeback after breaking her right arm last year, became the oldest woman to win a world championships medal, taking her haul to seven.
Vonn has had only five World Cup events back since the injury that left her without full use of her right arm but still managed a 77th World Cup win at Garmisch last month.
"It feels really good," she said. "I would have loved to ski a little bit faster but I fought really hard.
"It's been a difficult season coming back from a broken arm and the hand has given me a lot of trouble... it is what it is."
Italy's Sofia Goggia missed a medal, possibly gold, after several errors on the lower section cost her time.
Goggia was flying but crossed her skis and was lucky to avoid a high-speed crash. She finished fourth, 0.07 seconds behind veteran Vonn.
(Writing by Martyn Herman; Editing by John O'Brien/Sudipto Ganguly)
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