By GREG BEACHAM
After Varlamov stopped both Slovak attempts in the shootout, Kovalchuk beat Jan Laco to seal the Russians' second win in the preliminary-round.
Laco was a surprise starter in place of his winless team's two NHL goalies, and the Kontinental Hockey League backup nearly stole a win over the powerful Russian offense by making 36 saves.
Russia will find out whether it must play a qualifying game after Canada's late game against Finland.
But perhaps the Russians shouldn't be worried: After all, Canada was forced to play a qualifying game in its home Olympics four years ago, eventually rolling through four elimination games in Vancouver to win gold.
A day after the Russians' 3-2 shootout loss to the unbeaten U.S. team, they got enmeshed in a tense, defense-dominated game with Slovakia, which lost its first two games in Sochi in embarrassing fashion. The Slovaks fell 7-1 to the Americans before allowing tiny Slovenia to record its first Olympic victory.
Another boisterous sellout crowd at Bolshoy Ice Dome grew increasingly nervous as the deadlock stretched deep into the third period, but the Russian stars delivered in the shootout.
After Radulov beat Laco with a diabolical top-shelf backhand, Kovalchuk deked Laco to the ice and beat him easily to the stick side. Kovalchuk, who missed the final minutes of the second period with an apparent right leg injury, kissed his finger as he skated away to deafening cheers.
Russia also got a stellar game from Varlamov, who started the opener and but sat behind Sergei Bobrovsky for the loss to the U.S. Varlamov stopped Milan Bartovic twice on a breakaway chance late in the second period.
The Russians had no time to stew over their narrow loss to the Americans -- or that disputed call on a disallowed Russian goal in that game. Slovakia immediately mired the Russians' beautiful offensive game in a tight-checking positional contest that magnified every scoring chance and resulted in several injuries.
Russia's desperation increased in the third period, outshooting Slovakia 15-2 and barely missing on numerous scoring chances. Laco turned them all away, and defenseman Andrej Meszaros saved the game early in overtime by blocking Alex Ovechkin's rebound attempt at an open net.
The Russians finished the preliminary round with one win, one overtime win and one overtime loss. The top four teams in the preliminary round advance to the quarterfinals, and the remaining eight teams play a qualifying game to determine who else gets to the quarterfinals.