The U.S. went into the knockout match undefeated and outscoring opponents 9-2 at the Paris Games under new coach Emma Hayes but Japan foiled the Americans with steady defense.
Rodman's goal to the top of the far post came as time in stoppage time in the first extra period. She fell to the field as she was embraced by her teammates in celebration.
It was Rodman's third goal of the tournament. She nearly scored again in the second extra period.
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Former U.S. women’s national team stars Megan Rapinoe and Mia Hamm, as well as rapper Snoop Dogg, were among the fans at a packed Parc des Princes.
Hayes, the former boss at Chelsea, was hired last fall to lead the Americans after they struggled at last summer’s Women’s World Cup and were eliminated from the tournament earlier than ever before.
Japan had two good chances in quick succession in the first half. Mina Tanaka’s attempt was smothered by U.S. goalkeeper Alyssa Naeher before Miyabi Moriya blasted a shot from 12 yards that went over the goal.
Mallory Swanson, who leads the team with three goals in the tournament, had the best opportunities for the United States in the second half. But the U.S. was uncharacteristically plagued with errant passes and missed opportunities.
Rodman’s blast after a free kick in the 90th minute bounced off of a Japanese defender and was cleared away.
