Croatia's silver medallist Ivica Kostelic paid tribute to the champion after watching him nail the slalom set by his father Ante Kostelic, considered the most idiosyncratic of setters on the circuit.
Viletta, 28, and with just one victory in the World Cup to his name, was just 14th after the downhill, but he skied the second-fastest run in the slalom to secure gold in a combined total of two minutes 45.20 seconds.
"The race today was just amazing," he said. "At the moment I cannot believe it's true.
"After the downhill, I knew the slalom specialists were less than one second behind me and I knew I had to risk all and do a slalom that was just a perfect run for me."
For the 34-year-old Kostelic, it was a fourth Olympic silver and third in the combined, the Croat finishing just ahead of Italy's Christof Innerhofer, who took his second medal at these Winter Games after downhill silver on Sunday.
Kostelic hailed Viletta's slalom verve and was quick to defend his father Ante's course setting.
"I know there has been a lot of discussion over his course setting," Kostelic acknowledged.
"I'd just like to say that his course setting is somewhat old-fashioned, the way the courses used to look like before the measuring was introduced into the World Cup," he said.
"Since that time everyone became a course setter because all you need today is just a measuring tape and a drill and you're a course setter."
Kostelic added that Sandro "deserved this victory because he skied this slalom very well."
Viletta admitted: "For me it was a perfect slalom, a very good course."
The story of the day was almost more about who didn't make the podium than who did.
Defending Olympic champion Bode Miller and reigning world champion Ted Ligety were unable to break the US men's medal drought in the alpine events, while French tyro Alexis Pinturault skied out.
And Viletta warned that the Swiss team could continue their medal charge after Dominique Gisin and Lara Gut struck gold and bronze in the women's downhill earlier in the week.
"The women have had a good year and we're coming back to a good position with the men's team," he said.
"It's great to see them win and get medals and I try to do the same."
Kostelic's silver added to an amazing family collection that now boasts 10 Olympic medals, sister Janica having won six, including four golds.
"We've had one of the worst World Cup seasons in my career," he said.
"We weren't considered favourites for a medal. But the Olympics are something special for me and my family and that's very motivating."
For Innerhofer, a bronze was completely unexpected. The Italian is plagued by back problems, almost choosing to skip the slalom run.
"Nice to be here again!" joked the triple world medallist from Garmisch in 2011, who does not even train slalom.
"I was almost without goals because I thought it would be really tough," he said.
"After the downhill today, there were six or eight people who could win a medal," Innerhofer said.
"I thought it was impossible to be with the first guys."