Kozlovsky was one of the most admired singers of his time, one of the rarities known for his range, technique, beauty of tone, and acting. As if that weren't enough, he also directed an opera company, occasionally singing lead roles there as well. He had a remarkable longevity, singing creditably even in his seventies. While his most familiar roles were from the Russian repertoire (he is credited for making the Simpleton in Boris Godunov a role for stars rather than comprimarios), he was also noted for his performances of Massenet's Werther, Wagner's Lohengrin, and Rossini's The Barber of Seville. His style was old-fashioned, particularly in the bel canto repertoire, where sometimes he permitted a performance to become mere showmanship, but even those who deplored his taste had to admit his technical facility.
He made his opera debut at Poltava in 1918 as Gounod's Faust, though he did not graduate from the Kiev Institute of Music and Drama for another two years. He began his nearly 30-year career at the Bolshoi in 1926, and he was soon one of its leading tenors, making his last appearance in a staged opera there in 1954. Kozlovsky also started his own opera company in 1938, occasionally appearing in the lyric repertoire there. He was awarded the prestigious designation of People's Artist of the U.S.S.R. in 1940. In 1956, he began an impressively long teaching career at the Moscow Conservatory, retiring in 1980. Even into his seventies he was singing recitals, and at public appearances, even one celebrating his ninetieth birthday, was willing to oblige his audience with a few lines, at least, showing an increasingly amazing vocal longevity.