Ilyashenko joined the Communist Party of the Soviet Union in 1945 and worked as the head of the editorial department of the newspaper "Moldova Socialiste". He then worked as an instructor and as a head of the sector of the Central Committee of the Communist Party of Moldavia from 1946 to 1948. He was the Deputy Head of the Department of Propaganda and Agitation of the Communist Party of Moldavia from 1948 to 1951. He served as heads of various departments from 1951 to 1966. From 1962 to 1963, he served as the Chairman of the State Committee of the Council of Ministers of the Moldavian SSR and served as Deputy Chairman of the Council of Ministers of the Moldavian SSR from March 1963. From 3 April 1963 to 10 April 1980, Ilyashenko served as the Chairman of the Presidium of the Supreme Soviet of the Moldavian SSR. He simultaneously served as Deputy Chairman of the Supreme Soviet of the Moldavian SSR from 1966. Ilyashenko was elected as a member of the Central Auditing Commission of the Communist Party of the Soviet Union at the 23rd Congress of the Communist Party of the Soviet Union. At the 24th Congress of the Communist Party of the Soviet Union, he was elected as a candidate member of the Central Committee of the Communist Party of the Soviet Union. He was also a member of the Supreme Soviet of the Soviet Union for the 7th and 8th convocations.