Aleksandr Khazin was born in 1912 in Berdichev, Ukraine, in an educated Jewish family. His father was an accountant, and his mother was a physician.
The Khazin family later moved to Kharkov, where Aleksandr completed a seven-year school. In 1927, he enrolled in an electrotechnical school, finishing his studies there in 1931. Afterward, Khazin found a job at the Kharkov Electromechanical Plant, where he became active in a literary circle. He began to write poems in 1930, and his first publications soon followed. He joined the All-Ukrainian Union of Proletarian Writers. Before the war, Khazin published several collections of poetry, but did not quit his factory job. He enrolled at the night school of the Electrotechnical Institute, from which he graduated in 1939. After his graduation, Khazin was sent to Leningrad, where he worked briefly as a structural engineer. However, a year later he returned to Kharkov, intending to devote himself to literature.
After the beginning of Operation Barbarossa on June 22, 1941, Aleksandr joined the army, serving as a correspondent for the frontline newspaper Znamya Rodiny and the divisional newspaper Bolshevistski Natisk. His contributions to Znamya Rodiny, which were presented as the works of the fictional soldier "Trofim Bomba", became popular among the troops. In early autumn 1942, Aleksandr Khazin was wounded during the Novorossiysk Operation. He continued to write poetry during the war, publishing a collection of verse titled Military Verses in 1942. This was followed by a second collection, Compatriots, in 1945. In the course of the war, Aleksandr Khazin was awarded the Order of the Red Star, as well as medals.
In 1945, Khazin returned to Kharkov and became a full-time poet, writing monologues, skits, and witty parodies. In 1946, he wrote Onegin's Return, a biting and amusing parody of the absurdities of postwar life in the USSR. The parody was published in the Zvezda and Leningrad journals, and became popular. It was performed on radio by the famous stand-up comedian Arkady Raikin. However, this text incurred the displeasure of the country's chief ideologue, Andrei Zhdanov, who proceeded to denounce it in a speech, after which Khazin fell into official disgrace. His subsequent literary career was plagued with difficulties, and his works were no longer published, his membership in the Union of Soviet Writers notwithstanding. In 1949, he moved from Kharkov to Leningrad. However, this move failed to improve his professional prospects, and his only source of income was writing texts for performers under the pseudonym "Balashov". Later, Arkady Raikin, the celebrated Soviet comedian, gave Khazin the job of head of the literary section of his Theater of Miniatures. The two became fruitful collaborators, and many witty remarks written by Khazin and performed by Raikin entered the popular lexicon.
In addition to a great number of sketches for performers, Khazin also wrote short stories and novellas. He published several books, including prose works, in the 1950s-1970s. Aleksandr Khazin died in 1976 in Leningrad.