She was nominated for the Ariel Award for Best Supporting Actress in 2012 for her role as Nina in the film La Otra Familia.

Norvind began her acting career at the age of 6 in a theatre production of Henrik Ibsen's A Doll's House, and in television on the telenovela Chispita.

Norvind's break came in at the age of 17 in 1987 with the role of Leonor Gutiérrez on the El Canal de las Estrellas telenovela Quinceañera.

After a few small roles in several other telenovelas, she starred in Cuando llega el amor and then took a break from television.

In 2006, Norvind completed the film that her mother had been directing and producing at the time of her death in May of that same year, titled Born Without, a documentary about severely handicapped Mexican actor and musician Jose Flores, who was born without arms and other limbs, yet supports his large family by playing the harmonica at various venues throughout Mexico.