After winning the International Mozart Competition of the Vienna State Opera in 1991, she received invitations for concert and recital appearances, most notably an all-Mozart recital on the stage of La Scala. She also made a recital recording with EMI Classics of Mozart arias that was an extraordinary success.
Quickly engaged by major opera houses around the world, she sang Blondchen in Die Entführung aus dem Serail, Madame Herz in Der Schauspieldirektor, the title role in Zaïde, Adele in Die Fledermaus, and Zerbinetta in Ariadne auf Naxos.
In 1992, Dessay debuted as Olympia in Offenbach's Tales of Hoffmann, and in 1993, she sang at the opening of the New Lyon Opéra. In the same year she joined the roster of the Vienna Staatsoper with a triumphant performance as Blondchen. She sang there in an acclaimed production of Tales of Hoffmann with Plácido Domingo, and as Sophie in Strauss' Der Rosenkavalier opposite Anne Sophie von Otter. Another Strauss opera was the vehicle for her debut at the Metropolitan Opera in New York in 1994, where she sang Fiakermilli in Arabella. Also that year, she added to her credits the Queen of the Night (Mozart's Magic Flute) in the Aix-en-Provence Festival, and the title role of Delibes' Lakmé at the Opéra-Comique in Paris. Dessay enlarged the scope of her repertory in the mid- to late '90s, singing Strauss' rarely heard Die Schweigsame Frau (The Silent Woman) on her home stage in Vienna, Stravinsky's Nightingale at the Châtelet under Boulez, and Ophelia in Thomas' Hamlet at the Geneva Opera. Since then she has added Offenbach's Orphée aux Enfers, La Sonnambula, Lucia di Lammermoor, Massenet's Manon, and Susanna in Le nozze di Figaro to her repertory. She has made a specialty of Bellini and Donizetti heroines, excelling in roles both comic (La Fille du Regiment) and tragic (Lucia). Her performances in those roles were featured in Live from the Met Simulcasts in 2008 and 2011, respectively. Her recital album, Vocalises, won a Diapason d'Or award and a Classique d'Or RTL in 1998. Despite the need for vocal cord surgery, which put her career on hold from 2002 until 2005, EMI's recording of Lakmé with Michel Plasson conducting and Dessay in the title role won the award for French Recording of the Year at the Victoires de la Musique Classique. Other releases include Offenbach's Orphée and a Mozart aria disc on Virgin. She has recorded both the original French and Italian versions of Lucia di Lammermoor. Her list of awards also includes the Opera News Award and the Laurence Olivier Award (both 2008), and her designation as a Chevalier of the Legion of Honor (2011). In 2013, Dessay retired from live operatic performance (her final role was as Massenet's Manon in Toulouse, France). But she has continued to record, taking on several projects beyond the scope of opera (something she had previously avoided). Her 2013 release, Entre elle et lui, was a duo project with veteran French film composer and jazz pianist Michel Legrand. In 2017, Dessay released Pictures of America, her first English-language album, featuring a program of selections from the Great American Songbook.