From the thirties onward her fame as a singer grew, she appeared in films and had her own TV show in an incredibly long career that extended from 1931 through 2000.

Largely self-taught, she had a warm contralto voice as her innovative behind-the-beat phrasing and emotional intensity that she put into the words she sang, served to turn novelty tunes and light songs into definitive, bolero-based treatments.

From the mid-1930s through the late 1940s, Naranjo shared stages with many prestigious visiting artists from around the world, including Ary Barroso, Carlos Gardel, Tito Guízar, Agustín Lara and Pedro Vargas, to become a notorious celebrity while her audience greatly increased.

She also made films in Venezuela next to Amador Bendayán and Alfredo Sadel, among other important artists, appearing in Romance aragüeño (1939), Misión atómica (1947), and A La Habana me voy (1949).

At this time, she received contract offers from Colombia, Cuba, Mexico, and Puerto Rico, but chose to stick around Caracas and raised a family instead of pursuing an international artistic career.