Born on 9 November 1907 in Stavropol to Ukrainian parents, Zozulya entered the Soviet Navy (then the Naval Forces of the Red Army) in 1925 as a student at the M.V.

Zozulya served as navigator of the training ship Komsomolets from January 1929 and the destroyer Uritsky from February 1930.

Upon graduation in November 1934, Zozulya became assistant to the chief of the sector dealing with the Black Sea theatre and flotillas of the naval department of the 1st Directorate of the General Staff.

In late September he commanded a detachment of sailors that ensued the crossing of the troops of the Neva Operational Group in the area of Moskovskoy Dubrovki.

According to an award citation, Zozulya, "never, even in difficult conditions, lost his temper or composure, displaying personal courage in the fight against the fascists."

A year later, Zozulya became chief of the Operations Directorate of the Main Naval Staff, and in July 1947 became commander-in-chief of the 8th Fleet.

As chief of the Main Naval Staff, Zozulya encouraged his subordinates to not rely on close supervision from superiors, in contrast to the top-down style of his predecessor, Vitaly Fokin, and was praised for his management ability by Navy Commander-in-Chief Admiral Sergey Gorshkov.