Her cousin, Louis Morris (originally Moritz), was a clarinetist for John Philip Sousa's band (1907–1921).

Her American début at the age of seventeen in New York City on January 26, 1921 was one of the musical sensations of the year.

Shortly after her New York début, she was presented with the Guadagnini violin which had been owned by the American violinist Maud Powell, who had died in 1920.

In March 1921, Morini made her first recordings for the Victor Talking Machine Company in Camden, New Jersey, accompanied on the piano by her sister, Alice.

In 1962, she and Isaac Stern, Zino Francescatti and Nathan Milstein appeared in a memorial concert for violinist Fritz Kreisler.

[3] Harold C. Schonberg, music critic of The New York Times, once described Morini as "probably the greatest woman violinist who ever lived", though that notion was not one that pleased her.

She received honorary doctorates from Smith College, Massachusetts, in 1955, and from the New England Conservatory of Music, Boston, in 1963.