Kurochkin completed cavalry courses in Petrograd in 1920, the year when he also joined the Russian Communist Party (Bolsheviks).

He commanded a cavalry regiment in the Polish-Soviet war and was involved in the suppression of the Tambov Rebellion in 1921.

From December 1943 until February 1944, he was the first deputy commander-in-chief of the First Ukrainian Front under Marshal Konev and was remembered for his planning of the bloody Korsun–Shevchenkovsky Offensive.

His last assignment of the war would be commanding the 60th Army from April 1944 through May 1945 which took part in the Lvov-Sandomierz operation and fought in Central Europe.

After his tour in East Germany ended in 1947, he took over as an assistant commander-in-chief of the Far Eastern Military District.