Thomas Greilinger got the Germans going in the Slovak capital Bratislava before Patrick Reimer netted with a backhand in the third quarter.
"We were dreaming about a win over Russia from the very beginning, there is hard work behind it. We have deserved this win," Reimer told reporters after the match.
In the second match, played in the eastern Slovak town of Kosice, Julien Vauclair gave Switzerland a 1-0 win over France in overtime.
Russia next meet Slovenia Sunday in a second Group A match while Germany play hosts Slovakia.
(Reporting by Martin Santa, editing by Mark Meadows)