As a young teenager, she was seen by choreographer Uday Shankar, who became an ardent promoter of her performances, and throughout the 1930s she captured the imagination of audiences across India.

She went on to a global career that attracted international critical attention and the respect of dance greats such as Shambhu Maharaj, Dame Margot Fonteyn, Martha Graham, and Merce Cunningham.

Balasaraswati, encouraged by an administrator at the Music Academy in Madras, established a dance school in association with the institution.

Later that decade, throughout the 1970s, and into the early 1980s, she visited the United States repeatedly and held residencies—as both a teacher and a performer—at Wesleyan University (Middletown, Connecticut), California Institute of the Arts (Valencia), Mills College (Oakland, California), the University of Washington (Seattle), and Jacob's Pillow Dance Festival (Beckett, Massachusetts), among other institutions.

Through her international engagements as well as her activities in India, especially in Madras, Balasaraswati not only exposed countless audiences to the traditional style of bharata natyam but also trained many new practitioners of the art form.

In a review in 1977, the New York Times dance critic Anna Kisselgoff described her as one of the "supreme performing artists in the world".