After a successful 1982 season, Kuznetsov moved to Dynamo Kyiv where he remained until September 1990. He won the Soviet Top League in 1985, 1986 and 1990, the Soviet Cup in 1985, 1987 and 1990, and the UEFA Cup Winners' Cup in 1985–86. He became regarded as one of the best defenders in Europe in the second half of the 1980s,known for his strong ball-winning skills and long-range shooting power.