Sofya Velikaya, Yuliya Gavrilova and individual champion Yana Egorian took the maximum of five points off Ukraine in all nine fights.
In the bronze-medal match, the United States - featuring Ibtihaj Muhammad - beat Italy.
The 30-year-old from New Jersey is the first hijab-wearing athlete to represent the US at an Olympics.
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Russia won Olympic gold in the women's team sabre, beating Ukraine 45-30 in the final in Rio.