In 1958 he created the role of The Doctor in Barber's "Vanessa". Tozzi was the recipient of three Grammy Awards: in 1960 the Grammy Award for Best Classical Performance, Operatic or Choral for "The Marriage of Figaro" with Erich Leinsdorf; in 1961 the Grammy Award for Best Opera Recording for Puccini's "Turandot", with Erich Leinsdorf; and in 1963 the Grammy Award for Best Opera Recording for Georg Solti's recording of Verdi's "Aida" (with Leontyne Price and Jon Vickers). Tozzi also sang the bass part in the recording of Sir Thomas Beecham's version of Handel's "Messiah" for RCA Victor in 1959.