Kovalchuk put Russia on the scoreboard at 14:17 of the second period when he swatted a loose puck past Italy goaltender Jason Muzzati. "We had a lot of scoring chances but you have to give credit to their goalie, he played a great game," Russia defender Sergei Gonchar said. "We stuck to our system even though the scoring wasn't there."
Kovalchuk set up Alexander Frolov for Russia's second goal with about six minutes remaining to give the hosts a 2-0 lead.
Alexei Morozov later scored a power-play goal with four seconds left in the third.
Russia, which improved to 4-0, had outscored its opponents 25-6 in three previous games. The hosts will next play Switzerland on Sunday.
In Mytischi, Morten Ask scored the winning goal 2:22 into overtime to lift Norway to a 3-2 victory over Austria in the relegation round.
With the victory, Norway earned two points and took the lead in the standings.
The four teams in the relegation stage play a round robin, with the top two remaining among world hockey's elite in 2008 and the bottom pair dropping down.
After a scoreless opening period, Robert Lukas scored first for Austria at 9:19 in the second period before Jonas Andersen and Anders Bastiansen put Norway ahead 2-1 within five minutes of each other.
Austria's Daniel Welser scored 2:26 into the third period, forcing the game into overtime. All but the overtime goal came on the power play.