Vasiukov scored his best result to date when he won the 1961 Belgrade Open, ahead of Svetozar Gligorić.
During his peak years, from the early 1960s to the mid-1970s, Vasiukov scored wins in individual games over many top Soviet players, such as Smyslov, Bronstein, Tigran Petrosian, Mikhail Tal, Paul Keres, Mark Taimanov, Efim Geller, and Lev Polugaevsky.