Russia, which came second in Sweden's group, were the big favorites in advance - and the team that started strongest.
The lead goal came in the ninth minute through Vasili Ponomaryov in boxplay.
But Germany bit off.
In the second period, they created several qualified chances, but the goal never came.
Instead, Russia went up to a 2-0 lead through Danil Bashkirov.
Three minutes into the final period came the reduction.
Russia was careless in their own zone and Florian Elias made the best use of it and shot in 2-1.
- Russia looked human today and not at all as we have seen them before, says SVT Sports expert Jonas Andersson.
It was a dramatic final minute when Germany pressed.
Russia was sent off with five minutes left - but a minute later the Germans got a player sent off.
Russia held off and are ready for the semifinals.