Immediately after having finished his studies, young Morozov received a contract as a leading baritone to the Kirov Opera (today's Mariinsky Theatre) and changed two years later to the leading opera house of the Soviet Union: the Bolshoi Theatre in Moscow.
Here he sang the great parts of Russian and Italian repertoire such as the title role in Eugene Onegin, Lionel in The Maid of Orleans (with Makvala Kasrashvili in the title role), Yeletzki in The Queen of Spades, Robert in Iolanta all by Tchaikovsky, Rimsky-Korsakov's Misghir in The Snow Maiden (also recorded as CD), Andrey Bolkonsky in Prokofiev's War and Peace, Conte di Luna in Il trovatore, Gérmont in La traviata, Rodrigo in Don Carlo all by Verdi, Sharpless in Puccini's Madama Butterfly and Silvio in Leoncavallos Pagliacci (on DVD with Galina Kalinina and Vladimir Atlantov).
Since his very successful debut as Onegin at the Wiener Staatsoper, Igor Morozov has also been singing in many famous opera houses and festivals in Western Europe and the United States: Teatro alla Scala in Milan, Deutsche Oper Berlin and Staatsoper Unter den Linden Berlin, Staatsoper Hamburg, Cologne, Bayerische Staatsoper Munich, Amsterdam, Copenhagen, Opernhaus Zürich, Teatro Massimo Palermo, Bregenzer Festspiele, Salzburger Festspiele, Boston Music Festival, Houston Grand Opera with conductors such as Lorin Maazel, Anton Guadagno, Carlo Franci [it], Pinchas Steinberg and partners like Edita Gruberova, Vesselina Kasarova, Francisco Araiza, Giuseppe Giacomini, Nicolai Ghiaurov, Matti Salminen the leading roles in operas like Mazeppa (Tchaikovsky), Rigoletto, Nabucco, Simon Boccanegra all by Verdi, Kovaliov in Shostakovich's The Nose.
He has become a well known singer for different works of Shostakovich (Thirteenth Symphony, Babi Yar, Michelangelo Suite, Lady Macbeth of the Mtsensk District).
Woody Allen chose his interpretation of "Iago's Dream" from Verdi's Otello for his 2005 film Match Point.