Kuznetsov, 17, played last season for Avto Yekaterinburg and helped his country win the 2014 World Under-17 Hockey Challenge in Sarnia, Ont., with a goal and an assist in seven games.
The Saskatoon Blades chose Czech defenceman Libor Hajek second overall. The Sudbury Wolves made Russian forward Dmitry Sokolov the No. 3 pick in the draft.
Order of selection in the two-round draft rotated through the Western, Ontario and Quebec major junior leagues using an inverse order of the regular-season standings in each league.
Of the 78 forwards and defencemen from 14 countries drafted Thursday, 21 were Russian. The CHL stopped drafting European goaltenders in 2013.
There were 15 players chosen who were also drafted by NHL teams on Saturday.