The 28-year-old Norwegian, who won downhill bronze in the first week at Sochi 2014, mastered the challenging super-G course in a time of 1 minute 18.14 seconds.
Andrew Weibrecht of the USA, super-G bronze medallist in Vancouver, went one better from four years ago, taking silver at 0.30 seconds.
Meanwhile, his fellow American Miller, hotly tipped for gold, had to settle for joint bronze with Canada's Jan Hudec, as both men finished 0.53 seconds behind Jansrud’s time.
“It means the world”
“I am floating and feeling great. It hasn't sunk in yet. I wasn't nervous at the start but things got a little too exciting when Andrew Weibrecht was going down,” said a euphoric Jansrud.
“It means the world to me. It's the biggest thing you can win. It's something I have worked for since I was a little kid, so I am just going to enjoy it,” he added.
Weibrecht, whose last podium in a major event came in the same race at Vancouver 2010, caused another surprise with his second-place finish.
Miller had long looked likely to emerge victorious. The US skier clearly meant business as he looked to open his Sochi 2014 account after finishing eighth in the downhill and sixth in the super combined.
And he attacked the course full on to lead after the first split and then kept up an impressive pace right to the finish.
However, Jansrud left no doubt gold belonged to him with an utterly dominant performance that put him fully half a second ahead of the US skier.
“I made mistakes and the snow is really difficult. It just peels away from you. I tried to build pressure on the first couple of turns but it's really steep up there,” said Miller.
However, the 36-year-old American, who is competing at his fifth Winter Games in Sochi, did set a new Olympic landmark, as he became the oldest Alpine skier to win a medal. His overall tally now stands at six.
Miller was not the only favourite to find the course challenging. Defending Olympic champion and current World Cup super-G leader Aksel Lund Svindal of Norway could only finish seventh.
The three-time Olympic medallist and World Cup super-G leader was the biggest favourite going into the race. However, he was once more out-skied by his compatriot Jansrud, who had also dislodged him from the podium in the downhill.
“I had four bad turns at the top, and this is where I left all the time,” he explained, before paying tribute to his compatriot, Jansrud: “To see him pull out his stuff today was really impressive.”
US skier Ted Ligety, last year's super-G world champion, finished 14th, while Italy's Christof Innerhofer, 2011 super-G world champion and already a double medallist in Sochi with downhill silver and super-combined bronze, skied out early after attacking an early turn too aggressively.
Two of the best performances came from a pair of young Austrians skiers. 22-year-old Otmar Striedinger finished just two hundredths of a second off the podium, with team-mate Max Franz a further five hundredths behind.
Meanwhile, Norwegian Prime Minister Erna Solberg, who was on hand to watch Jansrud’s triumph, hailed it as “a great day for Norway” and described the skier as “an idol” for all young Norwegians.