Kuznetsov was born to a working-class family in Ust-Usolka, Solikamsky Uyezd, Perm Governorate.

In April 1915 he was drafted into the Imperial Russian Army, taking part in World War I.

In March 1916 he completed officer training in Kazan, attaining the rank of a Podporuchik in July.

During September 1939, Komkor Kuznetsov participated in the Invasion of Poland as chief of the Vitebsk and Polotsk Army Groups.

In late August, he was sent to command the Southwestern Front's 21st Army, but his force suffered crushing defeat once more in the Battle of Kiev.

On October, he was appointed to command the Kharkov Military District, but reassigned to head the 1st Shock Army on 23 November, with which he took part in the Battle of Moscow.

The Front was disbanded on late February 1945, and Kuznetsov assumed command over the 1st Belorussian's 3rd Shock Army on 16 March.

The Army was involved in the urban fighting inside Berlin; On 30 April, one of its formations, the 150th Rifle Division, stormed the Reichstag.