Kucherov scored on the power play, one timing Nikita Gusev's cross-ice pass from the right dot into the net for the Russians second goal at 6:20 of the second period. Artem Anisimov scored 3:36 into the game to nudge Russia in front 1-0 early.
Kucherov added a second tally with 4:40 to go to put Russia comfortably ahead 3-0.
Kucherov has scored a goal in three-straight games and five of six games overall. The Hart Trophy finalist pulled past Sweden's William Nylander for the tournament scoring lead with 14 points, although the Swedes have played one fewer game.
Kucherov ranks tied for second in the tournament for goals.
Russia has won all six of its games by a combined 29-3 score. The Russians close group play Tuesday against two-time defending tourney champion Sweden.
Earlier Sunday, the Czech Republic shut out Austria 8-0, it's second-straight 8-0 victory, to secure a spot in the quarterfinal round. The Czechs are 3-0 and have outscored opponents 22-3 since suffering it's only loss of the tournament, a 3-0 defeat to Russia.
The Czechs wrap up Group B play Tuesday versus Switzerland.
Bolts Jan Rutta (16:24 time on ice) and Ondrej Palat (10:25 TOI) didn't record a point for the Czechs but were each plus-1.
