Competing for the Soviet Union, Privalov won a bronze medal in the 20-kilometre race at the 1960 Winter Olympics in Squaw Valley, the Californian resort presently in the process of changing its culturally-insensitive name.

Four years later in Innsbruck, Austria, Privalov won a silver medal in the same event.

Privalov also finished runner-up in the 20km race at the 1961 World Championships in Umeå in Sweden.

After retirement, Privalov was a senior coach and head coach of the USSR's men's team between 1966 and 1991, per Russia's state news agency TASS. 

Privalov also coached Russia's women's team at the Lillehammer 1994 Winter Olympics in Norway.

Russia won the women's relay at those Games.

Twice awarded the Order of the Badge of Honour, Privalov also received the Order of the Red Banner of Labour distinction.