Dmitry Kalinin was the hero scoring the winning goal, the second of the game, with just 56 seconds remaining on the clock to give Russia their fourth straight win of the tournament.
Russia's left winger Ilya Kovalchuk was quoted on the championship website as saying about the goal: "It was a huge goal for us. We want to win our group."
Russia's other goals scorer were Ilya Nikulin, Oleg Saprykin, Sergei Mozyakin and Vitaly Proshkin.
Russian coach Vyacheslav Bykov said after the game: "The Swedes made it tough for us out there. We didn't have the speed tonight and the passing wasn't up to par."
Russia face the United States in their next qualifying match on Saturday evening.