Mikhail Naumenkov scored the game-winning goal at 1:45 of the third period to lead Russia over Slovakia.
Ignat Zemchenko won an offensive-zone faceoff cleanly right onto the stick of Naumenkov, who quickly fired a shot over Slovakian goalie Juraj Simboch.
"I'm happy that it ended up going into the upper part of the net," said Naumenkov through an interpreter. "That goal was important, that's for sure. Luckily I was able to score."
Igor Ozhiganov and Nikita Gusev also scored for Russia (2-0), which will face Latvia in the lone Pool A game on Thursday night.
Milos Bubela scored the lone goal of the game for Slovakia (1-1). With just 32.5 seconds left in the first period, Bubela outbattled Russia's Danil Apalkov for the puck in the slot and fired a low shot past goalie Andrei Makarov.
After Naumenkov scored, Gusev added an insurance marker to put the game away for Russia.
"Two mistakes in the last period and they got two goals," said Slovakian defenceman Martin Gernat.
Makarov, who plays for the WHL's Saskatoon Blades, finished with 31 saves in the Russian net to record the win. Simboch stopped 37 of 40 shots he faced in goal for Slovakia.