Mudranov won the men's 60kg final with a golden score victory over Kazakhstan's Yeldos Smetov, putting Russia's reduced team on the medals table on day one.
"Our country has been subject to a lot of psychological pressure, so to win a gold medal on the very first day means a lot for my country," said Mudranov.
The IOC cut the Russian delegation by more than 100 athletes after an anti-doping investigation uncovered widespread state-sponsored doping. But it resisted ordered an all-out Russian ban over the investigation.
But Mudranov insisted he was always confident of being allowed to compete despite just landing in Brazil three days before competing.
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"Before the Games we were training in Portugal for 10 days and we arrived here on August 3.
"We were confident, we were sure it can't be that the whole country won't be allowed to compete in the Olympic games.
"The president of the IOC realised it would be unjust for the athletes who have spent their entire life preparing for the Games, and for some it will be their only Games.
Russia finished fourth in the medals table in London four years ago and despite their limited numbers, Mudranov is sure there will be plenty more Russian success in Rio.
"The country proved to everyone we can win gold. I am confident this is not the last gold medal.
"We came prepared. No one broke down under the psychological pressure."
The International Judo Federation (IJF) had been outspoken in backing Russian athletes' right to compete.
"We hope that by allowing participation of Russian athletes in Rio 2016, we will send out a positive message to all the young people who deserve to be given examples of friendship instead of examples of Cold War," the IJF said in a statement before the Games.
Japan's Naohisa Takato and Diyorbek Urozboev of Uzbekistan claimed bronze.