Ponedelnik first started playing for a local team, Rostselmash, in 1956. In 1958 he switched to SKA Rostov-on-Don and was invited to join the Soviet national team. In the 1960 European Championship, the only major Championship ever won by the Soviet Union, Ponedelnik headed home the winning goal in extra time in the final game against Yugoslavia. Ponedelnik retired in 1966 after gaining weight and undergoing surgery for appendicitis. He scored 20 (according to some accounts, 21) goals in 29 games for his country.
In later years, Ponedelnik worked as a coach, a sports journalist, an editor of a sports publication, and an advisor to the President of the Russian Federation. He has received numerous awards for his contribution to Soviet and Russian sport. He is married and has three children and four grandchildren.