Fourcade, who won the 12.5km pursuit on Monday, made one mistake on the shooting range but was too fast on the skis for his rivals, making short work of his one-minute penalty.
German Erik Lesser shot clean but had to be content with silver, finishing 12.2 seconds behind Fourcade, a result he "had not even dreamt about".
Russian Evgeniy Garanichev took the bronze, 34.5 off the pace, on his 26th birthday, having also missed one target.
"There is less pressure than during a pursuit because you're on your own, there was less pressure," Fourcade told a news conference.
Fourcade, who also won silver in the mass start at the Vancouver Games four years ago, almost fell on a downhill curve as unseasonably warm temperatures made conditions tricky.
However, he managed to stay on his skis, avoiding a crash that would certainly have deprived him of the title.
"The conditions were a little bit complicated in the bends today," said Fourcade.
"The important thing is to stay up, that's why I put my hand on the cover. It added a bit of suspense," added Fourcade, who had reached out to a protective barrier to steady himself at one point.
"I sort of did a Bode Miller," he said with a smile.
The overall World Cup leader had started his campaign in slightly disappointing fashion, taking sixth place in the 10km sprint, but he thrashed the opposition to win the pursuit and on Thursday he lived up to all expectations.
Emil Hegle Svendsen, usually Fourcade's fiercest rival, continued his disappointing Games as the Norwegian finished seventh, almost a minute behind the winner.
Ole Einar Bjoerndalen, who won the sprint on Saturday, was looking to secure a record-breaking 13th Winter Olympics medal but was never in the mix as he made one mistake at each shooting section to end 34th.
Bjoerndalen, a seven-times Olympic champion, heaped praise on Fourcade.
"He is a fantastic athlete, he is so strong. I am happy for him, he is one of the best ever," he told reporters.
Bjoerndalen's former rival Raphael Poiree had said on Wednesday he believed Fourcade was "the new Bjoerndalen".
France coach Stephane Bouthiaux said Fourcade had an incomparable capacity to focus.
"He knows that if he misses a target at the last shooting he loses the title and yet he manages to shoot without even thinking about it. Nobody else can do that," he said.
The Frenchman will now hope to add to his tally with the mass start, which is being held on Sunday, the relay and the mixed relay, and said the relay would be his top priority.
"I think now the goal is only the relay, there is a mass start and I will give my best, but then I only want to win medals with my mates," he said.
"We've been fighting together for four years and we want to all come back with a medal."