Nepomnyashchy would start his career as a footballer where his greatest achievement was to play as a striker for third tier Soviet football clubSpartak Samarkand. His career was however cut short due to health problems and he had to retire at the age of 25 years. This saw him move into physical education and coaching that would see him land a job within the football coaching sports committee of Turkmenistan from 1970 to 1978. By 1979 he would achieve his first assistant coaching job with third tier Turkmen football club Kolhozchi Ashkhabad and by 1982 he was named as their head coach where he led them to eighth in his debut season. By the end of 1983 Nepomnyashchy had returned to the Turkmenistan Sports committee until in 1984 when he was doing training courses in Moscow, he was asked by the Russian Office of football if he wanted to work abroad. Nepomnyashchy soon accepted the offer and was expected to provide training courses and assistance to developing countries such as Algeria, Tunisia and Suriname. Nepomnyashchy would find these trips as too frustrating and periodical in there planning until Cameroon offered him a concrete proposal. Initially Nepomnyashchy thought that the Russian funded aid would see him coach one of the Cameroon youth teams, however with the previous manager Claude Le Roy deciding to leave to join Senegal there was an unexpected vacancy for the senior Head coach position, which Nepomnyashchy took and signed a two-year contract with the team. At first Nepomnyashchy would struggle with the French language and had to use an interpreter, however he would eventually get his message across on what he wanted his team to do and they would qualify for the 1990 FIFA World Cup. Drawn in Group B they unexpectedly beat reigning champions Argentina as well as Romania to book their place within the last 16. After beating Colombia 2-1 in extra-time Cameroon eventually lost to England in the Quarter-Finals. While he was offered an extension to his contract, Nepomnyashchy decided to leave the team after his contract expired to take on a more lucrative position with the Chinese Football Association as a technical consultant. In the 1992–93 1.Lig season Nepomnyashchy would return to management with Turkish side Gençlerbirliği S.K. before joining another Turkish side in Ankaragücü the following season. After an uninspired time within Turkey he would move to South Korea where he had a successful spell with Bucheon Yukong where he won the 1996 Korean League Cup with them. After his time in South Korea ended he returned to Russia for FC Dynamo Stavropol where he acted as a consultant in 1999 before returning to Asia where he went on to manage several different clubs before returning to national team management when he coached Uzbekistan after having a successful spell with one of its clubs, Pakhtakor FK where he won the 2006 league title with them.