Sultanova was born in Baku. Her father was a geologist, and her mother was an English teacher. She studied at the Azerbaijan Conservatory from 1942 to 1944, and at the Moscow Conservatory, where she graduated in 1950. She remained in Moscow after graduating and lived there until her death. Her teachers included Evgeny Golubev and Vissarion Shebalin, who encouraged her to incorporate Azerbaijani folk tunes in her music. She was also mentored by Azerbaijani composer Kara Karaev.
