When he was at school Yevgeny Aleynikov competed in a variety of sports including trampolining, track sprinting, and cycling, before settling with rifle shooting. After school Aleynikov attended the Polytechnic Mining and Metallurgical Department before transferring to the Institute of Physical Education. His skills as a sport shooter soon became apparent and he was quickly called up to the Soviet national team in 1987. His first international success came at the 1991 World Shooting Championships where he won silver in both the 10 metres air rifle and the 10 metres air rifle team events.
In 1996 Aleynikov represented Russia at the Atlanta Olympics where he narrowly missed out on medal after finishing fourth in the 10 metres air rifle. Two years later he won gold in the 10 metres air rifle team event at the 1998 World Shooting Championships. He returned to the Olympics for the Sydney Games in 2000, this time coming home with a medal when he won bronze in the air rifle, in addition to finishing seventh in the 50 metres small-bore rifle, three positions event. At his third and final appearance at the World Championships in 2002 he won another team gold in the air rifle along with an individual bronze. Aleynikov later retired due to an injury but continued to work in the sport as both a commentator and a coach of the Russian youth team. His wife Lyubov Galkina was also a skilled rifle shooter who won three Olympic medals, including gold at the 2004 Athina Games.
Russian Federation