Seven of the U.S. team that started the Montreal semi-final had played in the deciding game in 2011, where they lost to Japan, and for many this will clearly be a last opportunity to triumph.
Japan and England meet in the other semi-final on Wednesday in Edmonton. The winner will move on to face the United States in the title game on Sunday in Vancouver.
The inventive and fleet-footed Americans were the superior side throughout an exciting game but the world's second-ranked side benefited from two crucial decisions by Romanian referee Teodora Albon.
They took the lead in the 69th minute when captain Carli Lloyd scored a penalty after Albon ruled that Annike Krahn had obstructed Alex Morgan. Replays showed the offence took place outside the box.
"It was clearly outside the area ... I'm very sad that this penalty decided the game. But what am I going to do though?" said German coach Silvia Neid, adding that her side's usually lethal attack that had scored a tournament best 20 times coming into the match had been below-par.
Minutes earlier U.S. defender Julie Johnston was adjudged to have pulled down Alexandra Popp but escaped with just a yellow card. Neid said Johnston had been the last defender and should have been sent off.
Germany's Celia Sasic - top scorer in the tournament - dragged the resulting penalty wide in the 63rd minute.
"I thought it was an unbelievable duel between two tremendous teams," said U.S. coach Jill Ellis, who declined to comment on the officiating.
The Germans, who had produced some storming performances earlier in the cup, were atypically sluggish and looked to be feeling the effects of last Friday's gruelling quarter-final against France, when they played 30 minutes of extra time.
Goalkeeper Nadine Angerer made two crucial stops early in the first half against an American side that started the tournament slowly but has been gaining momentum and confidence.
U.S. substitute Kelley O'Hara flicked the ball home from close range in the 84th minute to seal a merited victory in front of a passionate Montreal crowd of more than 51,000, most of them Americans.
"Four years ago we came so close ... I feel we have really good momentum going into this," said Lloyd, 32, who played in the 2011 final.
Other survivors from that match who are in the current squad include keeper Hope Solo, 33, defender Christie Rampone, 40, midfielder Shannon Boxx, 38, and veteran forward Abby Wambach, 35.
(Editing by Steve Keating)
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