The 27-year-old Wild had already caused a minor upset by winning the parallel giant slalom title three days earlier. Although Slovenia's Zan Kosir ran him close in the final of the slalom, the Russian emerged triumphant once more, much to the pleasure of the home contingent in the crowd at the Rosa Khutor Extreme Park.
Four-time world champion and Vancouver 2010 silver medallist Benjamin Karl of Austria won the bronze medal, seeing off the challenge of Italy's Aaron March in the small final.
Perspiration plus inspiration
It was a historic double for the American-born Wild, who had already claimed the title in the parallel giant slalom title three days earlier.
And he credited his strong showing in Sochi to an intensive spell of off-season training.
“This is beyond believable. When I came to the Olympics and showed up I had already won,” he said.
“To win the other day was the greatest feeling of my life. I can't believe it. All those power drills I did in the summer, they really paid off. Nobody could keep up.
“It has taken a lot of hard work, man. When everyone else in the summer is taking vacation, I am working hard. I train, I train, and it paid off.”
In the early rounds of the competition Wild was on a different level to most of his rivals.
In the qualification and elimination rounds he was a second quicker than the others while he was almost two seconds faster than his last-16 opponent over the two runs.
But his real moment of brilliance came when he was pitted against Karl in the semi-finals.
Wild made a mistake on the first run meaning that he was hit with the maximum deficit of 1.12 seconds ahead of the second run.
His double hopes seemed over but he then produced a startling run to claw back all of the deficit, and surge ahead and into the final.