Canadian veteran Erik Guay, bidding to follow his gold in the super-G, was second, and Austria's Max Franz third.
After compatriot and reigning world champion Patrick Kueng and Norway's Kjetil Jansrud had set identical times to lead, 30-year-old Feuz produced a powerful descent down the icy course to go 0.39 seconds quicker.
He then watched anxiously in the finish area as Guay went quickest on the intermediate split times but finished 0.12 seconds slower. Franz was 0.37 seconds slower.
Among the thousands of Swiss fans celebrating in the finish area was tennis great Roger Federer, who last month won an 18th grand slam title at the Australian Open.
The blue riband race, cancelled on Saturday because of poor visibility, began from a lower start gate after clouds again made the top section too dangerous.
(Reporting by Martyn Herman; Editing by Hugh Lawson)
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