Kirsten's mother was an organist and music teacher, her grandfather was a conductor, and her great-aunt, Catherine Hayes, was also an opera singer. She left high school at age 16 and worked for the Singer Corporation sewing machine company and for New Jersey Bell, studying voice in her spare time. Her teacher, Louis Darnay, eventually employed her as a secretary and maid.
By the late 1930s she had an ongoing professional career as a radio singer on WINS, a member of the Kate Smith Chorus, and as a vocalist for pop orchestras. She mentored under Grace Moore from 1938, who had her study in Rome with Astolfo Pescia. Her time in Europe was cut short by the outbreak of World War II, and she returned in 1939, debuting at the New York World's Fair. Roles followed at the Chicago Grand Opera Company (Manon, 1940), San Carlo Opera Company (1942), New York City Opera (1943), San Francisco Opera (1945), and New York Philharmonic (1945). Her radio program "Keepsakes" ran for a year in 1943-44.
Kirsten joined the roster of principal sopranos at the Carmen with Bruna Castagna in the tile role. She also toured with company to Cleveland singing Mimì. In February 1946 she traveled with PLSOC to Washington D.C. to perform Marguerite in Charles Gounod's Faust. In December 1949 she recorded Manon Lescaut with the world-renowned tenor Jussi Björling. Her final year performing with the PLSOC was the 1946-1947 season, portraying Cio-cio-san in Madama Butterfly and Juliette in Roméo et Juliette.
Kirsten debuted at the Metropolitan Opera with the role of Mimi in La Boheme on December 1, 1945, and continued to sing with the Met for the next thirty years. While she performed primarily in the United States, she did perform in Europe at times, and gave performances in the USSR in 1962, singing Violetta in La Traviata at the Bolshoi Opera. She sang in the American premieres of William Walton's Troilus and Cressida and Francis Poulenc's Dialogues of the Carmelites in San Francisco.
In addition to her operatic activities, she sang on radio with Frank Sinatra (co-starring with him in Light-Up Time), Bing Crosby, Nelson Eddy, and Perry Como. She also appeared in two films, Mr. Music (1950) and The Great Caruso (1951). Her last performance with the Met was on February 10, 1979 as the title role in Tosca.
She published an autobiography, A Time to Sing in 1982. She was married three times. Her first marriage was to Edward MacKayes Oates, with a divorce in 1949; the second to Eugene Chapman in 1951, who died three years later; and the third to neurosurgeon Douglas French, who died in 1989. She suffered a stroke on November 5, 1992, and died of complications on November 18, 1992. Her papers are currently housed at the Howard Gotlieb Archival Research Center at Boston University.