Kuzmina won in a time of 21:06.08, Olga Vilukhina of Russia took silver, finishing 19.9 seconds behind the champion, Vita Semerenko of Ukraine took bronze, 21.7 seconds behind.
Slovenia became the surprise of the 2014 Olympic men's hockey tournament by posting a 3-1 win against Slovakia. For the first time in their nation’s history, Slovenia won an Olympic hockey game.
After two scoreless periods, Slovenia came to life early in the third and then held off a furious Slovakia rally.
Slovakia's ice hockey men's team failed, while the United States made a powerful statement of intent in the Olympic men's hockey competition with a 7-1 demolition of Slovakia in the opening Group A game.
Fourth seed Li Na won her second Grand Slam title after beating 20th seed Dominika Cibulkova in the Australian Open women's final (7-6 6-0).
Dominika Cibulkova after loss in final: "It's a big moment for me, I think I'm gonna cry....Will thank my coach, my boyfriend for all the support, my family back home. Will congratulate Li Na, she deserved to win."
World No.24 Dominika Cibulkova will play China's Li Na in the Australian Open final after both scored comfortable semi-final victories on Thursday.
Cibulkova, of Slovakia, belied the seedings in her 6-1, 6-2 defeat of Poland’s Agnieszka Radwanska to make her first grand slam final.