Prausnitz did not make a career of conducting, although he made guest-conducting appearances in the United States and Europe, where he lead the BBC Symphony and London's New Philharmonia Orchestra. He was on the faculty of the Juilliard School, the New England Conservatory, and the Peabody Institute in Baltimore.
The German-born Prausnitz was known for his controversial promotion of contemporary music and of Mahler, whose music then rarely performed. In the 1950s, he was forbidden by Juilliard president William Schuman from including Mahler's work in a program during the orchestra's tour of Europe.
"I had to sneak in the adagietto from Mahler's Fifth Symphony in as an encore," Prausnitz said. In 1974, the Bruckner Society of America awarded him the Gustav Mahler Medal of Honor.
Other composers championed by Prausnitz include Carl Ruggles, William Walton, Elliott Carter, and Roger Sessions, who all appear in his infrequent recordings. His books include Roger Sessions: How a "Difficult" Composer Got That Way.
While serving as music director of the Syracuse Symphony Orchestra, his programming included such works as Sessions' Ninth Symphony (dedicated to Prausnitz). While critics appreciated his leadership, the orchestra's board and financial backers were less pleased. Prausnitz left the ensemble in the mid-1970s.
Prausnitz joined Peabody in 1976 as the school's conductor of symphony and opera orchestras, and later became director of its conducting program and conductor of its Contemporary Music Ensemble. He stayed at the school for 21 years, until his retirement.