Kuzmina recovered from a 22-second deficit after the first round of shooting to roar to victory at Whistler Olympic Park in the first day of competition at the Vancouver Games.
The 25-year-old Kuzmina, who had never won a World Cup event, completed the course in 19.55.6, 1.5 seconds ahead of German Magdalena Neuner, 23, who in 2008 became the youngest ever women's World Cup overall champion.
"It's a big surprise," Kuzmina said after winning Slovakia's first-ever Winter Games gold. "I didn't expect to win. I was absolutely sure that Magdalena would be here."
Marie Dorin of France took the bronze in her first Olympics, hitting all 10 targets.
In a slight drizzle on Whistler Mountain, the 5-foot-10 Kuzmina, a silver medallist at the 2009 World Championships, had one penalty on the prone shooting but was flawless on the second to win the first biathlon gold of the Games.
Neuner admitted she was shocked by Kuzmina's triumph, calling her "unknown" but said she was surprised to win the silver.
"I gave everything I had," she said. "If only I could have gone a little faster. I fought for it."
The German admitted to running out of gas in the late stages of the race.
"I lost strength in the last leg," she said. "And I made a mistake in the last shooting.
Dorin, 23, may have another shot at a podium finish as the French team were expected to shine in the relays.
"I'm very happy with the standing shooting because even though my legs were shaking I managed to hit all five," said Dorin. "And I was very well on the skis."
World Cup leader Helena Jonsson of Sweden came home in a disappointing 12th in 20:42.5, nearly 47 seconds behind the winner, despite perfect shooting.
Kuzmina, a police officer as well as a biathlete, said her recipe for success was simple.
"Train, train and train again," she said with a smile.
Place of birth: Tumen,
Residence: Banska Bystrica, Slovakia
No previous Olympics results.
Other career achievements: Silver medallist, 2009 World Championships, 12.5km mass start
Kuzmina, who started the sport in 1999, is coached by her husband and Israeli cross-country skier Daniel Kuzmin. The Olympic gold in Vancouver was her first major title.
She switched allegiances from Russia to Slovakia in 2008 so that her son would be allowed to accompany her to national training camps.
Educated in law, Kuzmina works as a police officer as well as an athlete and a coach.