Raised by Traktor Chelyabinsk, Davydov joined the Soviet League powerhouse CSKA Moscow in 1986. He would play for CSKA until 1991-92, where he split the season between CSKA and the Winnipeg Jets, who had drafted him 235th overall in the 1989 NHL Entry Draft. Davydov did well with the Jets that season, scoring thrice and adding four assists for seven points in twelve games. The next season, he played his first full NHL season, tallying 28 goals and 21 assists in 79 games. From then on however, his NHL career started declining. Member of the original Florida Panthers squad, Davydov was traded halfway through the season to the Ottawa Senators. He had only 20 points in 61 games that season. He would play his last three NHL games in 1994-95, as he spent most of the season in the International Hockey League.