Norwegian Kjetil Jansrud took a surprise silver, the first major medal of his career, and compatriot Aksel Lund Svindal plundered his third of the Games with bronze.
Janka was the first Swiss man to win the Olympic giant slalom title since Max Julen at the 1984 Sarajevo Games. The Austrians had dominated the discipline at the last three Olympics.
"Its fantastic, I think I don't realise it yet. It's such a great thing to be Olympic champion and I am just 23 years old, its just amazing," said Janka, who beat Jansrud by a comfortable 0.39 seconds with the snow starting to fall.
"You must always take a lot of risks to win, I made no big mistakes from top to finish and that was the key today," added the Swiss, whose gold was his country's second in four men's Alpine races after Didier Defago's downhill victory.
Despite his first gold, he kept the celebrations as professional as a Swiss banker dealing in the precious metal - casually clenching his fist and barely smiling at the finish.
Jansrud had been only 11th after the first leg but, pressure off, he put in a storming second run to go from also-ran to fist-pumping gold medal contender.
"To have our first double podium here in the Olympic Games is unbelievable but I am just so happy I was above him," said Jansrud of Svindal, adding a bronze to his gold and silver.
While the Austrian women have won a gold and a bronze, the men have yet to medal.
They came pretty close, however, with Marcel Hirscher placing an agonising fourth, Romed Baumann fifth after ending the first leg just 0.02 behind Janka and Benjamin Raich sixth.
Raich's hopes of defending his title effectively ended when he hit a gate on the second run and was thrown off balance.
"I was having a good run but then I made that mistake," he said as Swiss fans celebrated around him with clanging cowbells. "Of course, it's disappointing for us and our fans but I did my best.
"We have one race left to do and we should be strong in the slalom," he added.
American Bode Miller's hopes of a fourth medal in four races disappeared when he skied out in the first run.
Britain's Ed Drake finished 37th, his final event at Whistler Creekside, one place behind top British finisher Andrew Noble, while Dave Ryding was a distant 47th after tangling with a gate during his second run.
Place of birth: Obersaxen, Switzerland
Residence: Obersaxen, Switzerland
No previous Olympic results:
Gold, 2009 World Championships, giant slalom
Bronze, 2009 World Championships, downhill
Champion, 2008/09 World Cup, super combined
Runner-up, 2009/10 World Cup, super combined
A native of Obersaxen, a village of 800 people in Switzerland’s southeast, Janka joined the World Cup tour in December 2005 at Kranjska Gora at the age of 19.
Nicknamed the ‘Iceman’ for the calm way he has handled his rapid rise in the sport, he started skiing at two and later concentrated on the sport after being inspired by Austrian Hermann Maier’s performance at the 1998 Olympics.
He was a virtual unknown when he won his first World Cup race in December 2008, a giant slalom at Val d’Isere.
In December 2009, he became the first skier to claim three World Cup victories, in different disciplines in consecutive days, at the same venue since Frenchman Jean-Claude Killy in Franconia in 1967.
He won the super combined, downhill and giant slalom at Beaver Creek’s Birds of Prey course in Colorado.
The 23-year-old all-rounder is second in the overall World Cup rankings this season.