Baranov led the corps as part of the Western, Southwestern, Voronezh, and 1st Ukrainian Fronts in the Voroshilovgrad Offensive, the Third Battle of Kharkov, the Donbass Offensive, the Battle of Kiev, and the Zhitomir–Berdichev, Rovno–Lutsk, Proskurov–Chernovitsy, Lvov–Sandomierz, Eastern Carpathian, Vistula–Oder, Lower Silesian, Upper Silesian, Berlin, and Prague Offensives. He was promoted to lieutenant general on 15 September 1943. The corps was particularly distinguished in the capture of Zhitomir on 13 November 1943, receiving the name of the city as an honorific, and Baranov received the Order of the Red Banner for his leadership. During the Lvov–Sandomierz Offensive in July and August 1944, Baranov commanded a cavalry-mechanized group composed of his corps and the 25th Tank Corps. 1st Ukrainian Front commander Marshal of the Soviet Union Ivan Konev described him as a "brave and strong-willed general" in a December 1944 assessment, but tempered his praise by noting that Baranov was "insufficiently decisive and only fulfilled his assigned missions with the prodding of the front military council" during the Lvov–Sandomierz Offensive. For "successful completion of combat missions and the high combat efficiency of the corps," Baranov received the title of Hero of the Soviet Union and the Order of Lenin on 29 May 1945.