The Japanese, playing in their first semifinal, beat Sweden by the same score with a double from Nahomi Kawasumi, including a spectacular 35-metre lob, to book a spot in Sunday's final.
On a rainy afternoon, the Americans, who won the title in 1991 and 1999 and have never finished below third place in a women's World Cup, took an early lead when Lauren Cheney flicked in a Carli Lloyd cross in the ninth minute.
France levelled after the break with a Sonia Bompastor cross that bounced past US ’keeper Hope Solo but two goals in three minutes from Abby Wambach (79th) and Alex Morgan (82nd) secured a third World Cup final appearance for the Americans.
“This is our journey, this is our dream,” a beaming Wambach said. “France are a great team. There were moments they were outplaying us but I am so proud of this team.”
“I know we are going to pull through. I have belief in this team. Everybody is working for each other.”
In Frankfurt, captain Homare Sawa turned from villain to hero by putting Japan 2-1 up on the hour after her defensive error had given Sweden a 10th minute lead.
Josefine Oqvist pounced on Sawa's disastrous back pass, cut into the box and fired home from a tight angle but Japan recovered quickly as Kawasumi equalised nine minutes later after scrambling the ball over the line.
Sawa added the second with a close-range header after the Japanese had rattled the bar minutes into the second half and Kawasumi completed their comeback in style, catching Swedish ’keeper Hedvig Lindahl out with a spectacular lob.
