Baevsky joined the military in May 1940 after graduating from the Dzerzhinsky Aeroclub flight school in 1939. In November 1940 Baevsky was promoted to the rank of junior lieutenant and assigned as a flight instructor to the Serpukhov flight school. In 1941 he was transferred to the Chkalov Central Aeroclub in Northwest Moscow where he worked until he was sent to the front in April 1943 in the 5th Guards Fighter Aviation Regiment of the 1st Guards Mixed Aviation Corps of the 17th Air Army. His first experience of aerial combat was with a Bf 109 on 27 April 1943. During the war he participated in aerial combat in the Battles for Berlin, Kursk, Dnieper, and Warsaw; by December 1943 he had completed 144 combat sorties and was nominated for the title Hero of the Soviet Union which he received on 4 February 1944. By the end of the war he had completed 252 sorties in 52 different aerial battles, for which he became flying ace for having personally shot down 19 enemy aircraft in total while flying a Lavochkin La-5.