Yury Sharov took up fencing in 1953 and, after specializing in foil, won his first honours in 1955 when he became the Soviet junior foil champion. Sharov was selected to the Soviet national team in 1963 and was on the national team until 1972. Sharov was a solid team competitor who never fenced individual competitions at major international championships. With the Soviet team, Sharov won Olympic gold in 1964, captured Olympic silver in 1968, was the world team champion in 1963, 1965, 1966 and 1969, and won a team silver at the 1967 World Championships. He also helped win the European team cup in 1970 and 1971. Domestically, Sharov won his only individual Soviet foil title in 1964, and four team titles (1958, 1961, 1968-69).
After finishing his sporting career, Sharov worked as a fencing coach and judge in his hometown of Saratov. From 1972-84 he was the director and fencing instructor of sports school Trud in Saratov and from 1984-87 he was the fencing instructor with Saratov Polytechnic Institute (now Yury Gagarin State Technical University of Saratov). Starting in 1987, Sharov worked as a fencing instructor with Burevestnik Saratov, while serving as the president of the club from 1993-2013.