Yevgeny Yatsinenko competed in three major international tournaments during his career. At the 1956 Olympics, he was fifth in K2-10K with Sergey Klimov; at the 1957 European Championships, Yatsinenko won gold in the K-4x500 m relay with Igor Pisarev and non-Olympians Valentin Naumov and Aleksandr Markovtsev; while at the 1958 World Championships, Yatsinenko won silver in K2-1000 m with Ivan Holovachov. Yatsinenko also won eight Soviet titles – in 1958 in K1-10K, in 1960 in K-4x500 m relay, in 1957 and 1960 in K2-1000 m and in 1957, 1959, 1964 and 1965 in K2-10K. After finishing his sporting career, Yatsinenko worked as a kayaking coach in his hometown of Mykolaïv, Ukraine.