Six years after his only World cup victory to date on the same Italian piste, the 30-year-old American upset the favourites to win in one minute 28.82 seconds.
The organisers' decision to hold the race at all costs after two delays and an interruption helped the Park City speed specialist back on the podium for the first time in five years.
While Nyman is a specialist speedster, the lucky man on the day was Slovenia's Rok Perko, who finished second, 0.19 of a second adrift, for his first top 10 placing after seven years on the circuit.
In a race favouring late starters, world champion Erik Guay finished third, 0.24 behind Nyman.
Starting in much worse conditions with poor visibility, Norwegians Kjetil Jansrud and Aksel Lund Svindal finished fourth and fifth.
Svindal took his overall World Cup total to 585 points, leading American Ted Ligety by 177 points while holder Marcel Hirscher of Austria lies third on 380 points.
Heavy snowfalls forced two delays to the race and it finally took place two hours behind schedule on a shortened course to enhance visibility.
The classic Val Gardena downhill had been stopped last season because of gusty winds and the International Ski Federation clearly did not want it called off again.
But while the first 11 starters were able to complete the course safely, fog rose again above the tricky, bumpy Kamelbuckel section, forcing the organisers to halt the race for another half hour.