Neviarouski made his Olympic debut at the 2004 Summer Olympics in Athens, competing in two swimming events. In the 100 m freestyle, he challenged seven other swimmers on the fifth heat, including Lithuania's Rolandas Gimbutis, a member of the swimming team for the California Golden Bears. He edged out Greece's Aristeidis Grigoriadis to take the third spot by a quarter margin (0.25), with a time of 50.36 seconds. Two days later, Neviarouski placed second behind Hungary's Krisztián Takács, on the sixth heat of the men's 50 m freestyle by one hundredth of a second (0.01), clocking at 23.13 seconds.