MANCHESTER, England (AP) — Japan and the United States made it through the semi-finals of the women’s Olympic football tournament yesterday, setting up a rematch of the World Cup final won by the Japanese just a year ago.

Japan beat France 2-1 in London and the United States defeated Canada 4-3 in extra time in a thrilling match at Old Trafford in Manchester.

The US will be going for revenge and their third-straight gold medal. Japan will be playing in their first Olympic final to try to show their World Cup win was not a fluke.

Japan opened a two-goal lead against France and then held on for the victory, surviving a missed penalty kick by the French in the final minutes.

The US came from behind three times to send the match against Canada into extra time, then got an injury-time winner from Alex Morgan to advance. She headed the ball into the net after a cross by Heather O’Reilly as time was about to expire, putting the US in the gold medal match for the fifth straight time.

“This team refuses to lose and always finds a way to win,” US coach Pia Sundhage said. “There is something special, about this team.”

Christine Sinclair scored for Canada in the 22nd, 67th and 73rd minutes, but the US rallied with goals by Megan Rapinoe in the 54th and 70th minutes and by Abby Wambach from a penalty kick in the 80th.

“If I’m sitting in the stands watching this game and not rooting for any team, it’s fantastic, it’s entertaining,” Sundhage said. “This is when it really matters, it’s not a friendly, it’s the semi-finals of the Olympics.”

The Americans have played in the gold medal match in every Summer Games since women’s football was introduced in Atlanta in 1996.

Canada were trying to secure their first top-three finish at an Olympics or World Cup. They were also trying to end a 26-match winless streak against the Americans. They had been eliminated by the US in extra time in the quarter-finals in Beijing four years ago.

Canada coach John Herdman loudly complained of the refereeing of Christiana Pedersen of Norway, especially in the penalty awarded to the United States. He didn’t think it was a hand ball and was in awe that Pedersen awarded an indirect free kick against goalkeeper Erin McLeod for holding the ball inside the area for more than six seconds. The indirect kick led to the hand ball.

“Two bizarre decisions. I’ve never seen a decision like that given. An indirect free kick without a real warning or a yellow card, just a bit random,” he said. “And then the handball when something just gets blasted at you.”

Japan reached their first Olympic final with the win over France at Wembley. Their best result so far had been a fourth-place finish in 2008 in Beijing, when they lost to the US in the semi-finals.

“Since 2008 we have had an objective to win a medal at the Olympics,” Japan coach Norio Sasaki said. “The attitude of the players to win this game was strong. The mental part makes the difference at this stage.”

It was the first time the Japanese entered a tournament as one of the main title favourites following their World Cup triumph in Germany last year. They had eliminated Brazil, silver-medallist in the last two Olympics, to make it to the semi-finals in London.

The Japanese looked set for a comfortable win over the French after goals by striker Yuki Ogimi in the 32nd and Mizuho Sakaguchi in the 49th. France pulled one closer with substitute Eugenie le Sommer in the 75th and had a chance to equalise with a penalty kick just a minute later, but midfielder Elise Bussaglia rolled her spot kick wide of the right post.