Germany's Erik Lesser took silver and Russian Evgeniy Garanichev won bronze on his 26th birthday, but there was disappointment for Norwegian veteran Ole Einar Bjoerndalen.
The 40-year-old failed in his bid to win Winter Olympic record of 13 medals when he finished in 34th after problems in the shooting section, where he picked four penalties.
"I wanted to show my rivals that I'm still angry," said Fourcade after his triumph, when asked if he was "focused" or "angry."
On a day when six golds were awarded, Justyna Kowalczyk of Poland won the women' s 10km classic style event in nordic skiing.
Kowalczyk, who started favorite, finished nearly 20 seconds clear of Charlotte Kalla of Sweden, with Therese Johaug of Norway in third place.
Away from the medal action, Russia's ice hockey men opened their campaign with a 5-2 win over Slovenia, while the United States thrashed Slovakia 7-1 and defending champions Canada beat Norway 3-1.
But there was disappointment for the host nation when figure skating hero Yvegeny Plushenko dramatically withdrew just before he was due to compete in the men's figure skating short program.
The 31-year-old had been personally congratulated by Russian President Vladimir Putin after helping his country to win the team gold Sunday.
A two-time Olympic champion, he was bidding to become the first man to win five figure skating medals at the Winter Games.