Detroit Red Wings forward Pavel Datsyuk netted Russia's winning goal, while goalkeeper Vasili Koshechkin made 26 saves to set up Russia's meeting with the other semi-final winners Czech Republic in Sunday's finale.
"It was a hard and nervous game but we won deservedly," Pittsburgh Penguins striker Evgeni Malkin said.
"I was happy to score today it was a really indispensable goal. We dominated the playing but couldn't score and it was our break-through goal."
Germany, supported by a capacity 18,734 home crowd, produced courageous hockey from the start, testing Russia's defence and trying to storm their way into the final.
Germany skipper Marcel Goc had his supporters on their feet, when he put his squad into the lead on two-man powerplay sending in a rebound after Felix Schutz's powerful shot 15:30 into the match.
In the second period the hosts, who were playing their first ever semi-final since the existing championship format was introduced in 1992, continued their brave performance, while Russia played nervously producing too many own mistakes.
But halfway into the match Russia seized the initiative to pull the scores level through Malkin, who beat 'keeper Robert Zepp with an unopposed slap shot. After the second intermission Russia took complete control but failed to convert their supremacy into goals before 58:10 when Datsyuk picked the puck in Russia's zone and skated towards Germany's net to wrist it home from the left face-off circle.
Germany coach Uwe Krupp substituted his goalie for the sixth field player with 1:30 to go but the hosts failed to level.
"We expected Germany to play defensively but our unforced mistakes and penalties allowed them to score," Washington Capitals striker Alexander Ovechking said.
"We were self confident and stronger than the hosts but couldn't score for almost half an hour and that made us a bit nervous. Luckily we managed to come back and win. But tomorrow we also expect a tough and even match."
German goalie Rob Zepp said: "I think we're more disappointed now than if we'd gotten blown out in the game."
"We had a chance to win right until the end. It's a very disappointing feeling, but when we step back from it, later tonight or tomorrow morning, I think we have a lot to be proud of."
Earlier Czech Republic battled back from a goal down for a 3-2 win over Sweden in a penalty shootout.