Michael Wolf scored Germany's first goal while goal tender Dennis Endras recorded 31 saves to give his side a morale-boosting win.
"It's an unbelievable feeling when you're playing in front of a 76,000 home crowd," Wolf said. "Such fantastic support drives you crazy and boosts your performance a lot. We just couldn't play badly today."
Teammate Sven Butenschon added: "It felt more like a World Cup soccer game than a hockey game. When you hear the roar of (so many) people, it is a different noise."
US team captain Jack Johnson praised German keeper Endras but added that his team had plenty of time to make amends for the shock defeat.
"I don't think we played poorly," he said. "It was their goaltender who played really great today. It's a long tournament. We can still walk out of here with a gold medal. And that's our attitude."
Championship organizers relocated the opening game to the Veltins-Arena in Gelsenkirchen, home venue of the Bundesliga football club Schalke 04.
The 76,152-seat arena was transformed into an ice-hockey venue and was sold out to set a world record attendance for an ice hockey match, breaking the previous best of 74,554 spectators, set in the United States at a 2001 game between Michigan State University and the University of Michigan.
The previous highest figure for the world ice hockey championships was 55,000 spectators set in 1957 in Moscow at the deciding game between the Soviet Union and Sweden.
Germany started in a lively style trying to take the US team's goal by storm, creating a set of scoring chances when St Louis Blues forward T.J. Oshie was sinbinned for hooking, but the visitors defended well and kept their net clean.
The Americans soon took the initiative back. They outshot their rivals 8-7 in the opening period keeping Endras under pressure but also failed to find the net before the first intermission.
But it was Wolf who netted the opeining goal 5:20 into the second period wristing home a rebound from the right face-off circle after Marcel Muller's sharp-angled shot.
US players rushed ahead seeking an equalizer but the German defence played without any noticeable mistakes to stifle the Americans' attacks at the far approaches to their net.
In the third period the US team stepped up a gear and began peppering Endras with shots and Ryan Carter of Anaheim Ducks pulled the score level at 48:28, sweeping the puck in between the 'keeper's pads despite tough physical opposition from defender Nicolai Goc.
The Americans dominated play in the remaining regular time but failed to score a winning goal. Schutz stopped the time just 21sec into the overtime tipping teammate Constantin Braun's shot from the blue line past US netminder Scott Clemmensen.