He was elected a candidate member of the Presidium (as the Politburo of the Central Committee of the Communist Party of the Soviet Union was then called) on 14 February 1957 and served as a full member from 29 June 1957 until he was relieved of his duties on 16 November 1964, following the ousting of his mentor, Nikita Khrushchev a month earlier.
As the Time cover illustrated shows, he was for many years thought to be Khrushchev's likely successor as the dominant figure in the Soviet hierarchy of power. This was clearly what Khrushchev had intended, but even before his mentor's removal from office in October 1964 Kozlov's position in the Soviet hierarchy had been undermined by the effects of his alcoholism; in 1963 he had ceased to be Secretary of the Party. At the time of his resignation in November 1964, Kozlov was already seriously ill after a stroke and died two months later. He was buried in the Kremlin Wall Necropolis, which indicates that he was not in deep disgrace under Brezhnev (later, neither Khrushchev nor Mikoyan were allowed to be buried there).