Krasovsky was drafted into the Imperial Russian Army at 1916 and participated in the First World War as a communications NCO in an air unit. Soon after the October Revolution, he joined the Red Guards, and later - the Red Army.
Joining the Communist party on 1918, Krasovsky became an observation pilot, and was appointed commander of the 4th Army's air detachment on October 1919. He took part in the Civil War, fighting in the battles against Admiral Kolchak.
After a diverse service in the Air Force, Krasovsky graduated from the Zhukovsky Air Force Engineering Academy at 1936. Afterwards, he supervised the Leningrad Military District's air component.
During the Soviet-Finnish War, he commanded the 13th Air Army. At 4 June 1940, while supervising the Krasnodar Military Flight Academy, he was promoted to a major general. On June 1941, he was the chief of the North Caucasus Military District air component.
Soon after the German Invasion, Krasovsky was appointed commander of the 56th Army Aerial Detachment, on August 1941. He also commanded the Bryansk Front aerial units, and from November 1942 - the 17th Air Army, that participated in the Battle of Stalingrad. At 20 December that year, he was made a lieutenant general. From March 1943, Krasovsky headed the 2nd Air Army, an office he held until the war's end. His forces took part in the battles of Kursk, Eastern and Western Ukraine, Silesia and Berlin. On 4 February 1944, he was promoted to Colonel-General. On 29 May 1945, he was awarded the title Hero of the Soviet Union.
Until 1947, Krasovsky remained the commander of the 2nd Air Army. Then, he was assigned as chief of the Air Force in the Far East. In September 1951, he was sent as an advisor to the Chinese Air Force for a year. After a further year as the commander of the Air Forces of the Moscow Military District, he returned to his former duty in the North Caucasus once more.
From 1956 until retirement at 1968, Krasovsky was the commander of the Gagarin Air Force Academy, receiving his final promotion to Marshal of Aviation on 8 May 1959. He was also a member of the Central Auditing Commission from 1961 to 1966. In July 1970 he was called from retirement to serve as an inspector in the Ministry of Defense.