Glaz studied at the State Academy of Music in her hometown of Vienna and later at the Mozarteum in Salzburg. She made her opera debut at the State Opera of Breslau as Erda in Wagner's Das Rheingold in 1931, at age 19, before touring Austria and Scandinavia and performing at the German Theatre in Prague.
The rise of the Nazis obliged her to leave Europe. Following an American tour with the Salzburg Opera Guild in 1936 she emigrated to the U.S., where she sang with the Chicago Opera and in concerts conducted by Otto Klemperer in Los Angeles. She became a U.S. citizen in 1943.
At the Metropolitan Opera between 1942 and 1956, she sang such roles as Annina in Der Rosenkavalier and Mary in Der fliegende Holl‹nder.
She taught at the Manhattan School of Music, starting in 1956, and in New Haven, Connecticut, where she founded the New Haven Opera Society.
In 1977 Hertz and her husband, Dr. Frederick Redlich, then chairman of the Yale's department of psychiatry and later dean of the university, moved to Los Angeles. Glaz was appointed to the faculty of the University of Southern California, where she taught until 1994.