Novoa made his operatic debut with the Instituto Nacional de Las Bellas Artes in Mexico City, in 1960, as B.F. Pinkerton in Madama Butterfly.
His first great success occurred in 1967, when he created the role of Pier Francesco Orsini in Ginastera's Bomarzo, for the Opera Society of Washington.
He began his tenure with the New York City Opera in 1966, where he appeared regularly until 1972, in Tosca (with Sherrill Milnes as Scarpia), Carmen (opposite Huguette Tourangeau), Gianni Schicchi (with Norman Treigle and Beverly Sills), Der Rosenkavalier (with Elisabeth Grümmer), La traviata, Bomarzo (in its New York premiere), Lucia di Lammermoor (with Sills), Don Rodrigo (of Ginastera), and Mefistofele (with Treigle).
In 1974, Novoa sang in a Concert Version of Mefistofele, alongside Treigle and Nancy Shade, at London's Royal Festival Hall.
The tenor also sang with major companies in Buenos Aires (Bomarzo at the Teatro Colón), Toronto, Vancouver, Marseille, Stuttgart, Boston, Chicago, Cincinnati, Fort Worth, Houston, Omaha, Philadelphia, Portland, and San Diego.