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Mudranov is one of 271 Russian athletes competing in Brazil despite calls for a blanket ban on the country following evidence of state-sponsored doping.
He beat reigning world champion Yeldos Smetov, who eliminated Great Britain's Ashley McKenzie, in the final.
Meanwhile, Argentina's Paula Pareto added the Olympic crown to her world title by winning the women's -48kg.
Pareto, 30, beat South Korea's Bokyeong Jeong to claim her nation's first medal of the Games in neighbouring Brazil.
Later on Saturday, three-time European champion Mudranov, 30, won his first Olympic medal in a tight final against Smetov.
Neither man scored in the initial five-minute contest, with Mudranov eventually winning just 44 seconds into the golden score decider.
Smetov, 23, had earlier ended McKenzie's hopes of becoming Britain's first male judo medallist since Raymond Stevens at Barcelona 1992.
The 27-year-old from Surrey is ranked 20th in the world and was an outside medal chance.
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Russia claimed its first medal of Rio 2016 as Beslan Mudranov won Olympic gold in the judo men's -60kg.