In 1976, she performed Tosca with Luciano Pavarotti at the Lyric Opera of Chicago. Reportedly, she has sung this part over 400 times during her career. Later in 1976, she sang the part of Minnie with Plácido Domingo for Queen Elizabeth's 25th Jubilee Celebration at Covent Garden, which was filmed live and recorded.
In 1979, she made her Metropolitan Opera debut as Senta in Der fliegende Holländer. She has sung regularly with the Met in Tosca, Don Giovanni, Manon Lescaut, Un ballo in maschera, Falstaff and La fanciulla del West.
During her career, she has sung and recorded all over the world, including in San Francisco, Chicago, Los Angeles, New York City, Buenos Aires, Salzburg, Hamburg, Los Angeles and London. Her recordings include Musetta in La bohème, with Renata Scotto, Alfredo Kraus, Sherrill Milnes and Paul Plishka, for Angel/EMI, James Levine conducting (1979); La fanciulla del West, with Domingo and Milnes, Zubin Mehta conducting (DGG, 1977); Marietta in Korngold's Die tote Stadt, with René Kollo, Erich Leinsdorf conducting (RCA, 1975); Mahler's Symphony No.2 with Claudio Abbado and the Chicago Symphony Orchestra; and a special recording with Roger Wagner on Angel/EMI entitled "Magnificat." In celebration of the 100th anniversary of the Chicago Symphony Orchestra, a compact disc was issued of Miss Neblett singing in Mahler's Symphony No. 8, Levine conducting. Miss Neblett is featured in "James Levine's 25th Anniversary with the Metropolitan Opera" recording, singing the role of Alice Ford in Falstaff with Giuseppe Taddei.
Several of her performance have also appeared on television, including a tribute to George London at the Kennedy Center Washington, D.C. She also appeared as a guest on The Tonight Show with Johnny Carson.