At the 2012 Summer Olympics in London, Morozov was as a member of the Russian 4x100-meter freestyle relay team, that placed third behind France and the United States. Swimming the third leg, Morozov swum a split of 47.85. At the 2016 Summer Olympics in Rio, Morozov would fail to qualify for the final in both his individuals events, the 50m freestyle and 100m freestyle, finishing 9th and 10th respectively. Morozov would also compete in the Russian 4x100-meter freestyle relay, splitting a time of 47.35. The relay team would however place 4th after being out touched by Australia.