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Megan Rapinoe (two) and Alex Morgan connected for three of the US’s four goals.
MANCHESTER, England — The United States women’s soccer team usually dominates Canada, beating up on its neighbor to the north seemingly at will. In the previous 26 meetings between the teams before Monday’s Olympic semifinal at Old Trafford, the Americans had won 22. The closest the Canadians came to victory was four ties.
But here is what the Americans needed to record their latest victory: three deficits erased, two memorable shots from their enigmatic midfielder, and one arcing, penetrating, magical header from their superlative striker with just 30 seconds remaining in extra time.
Alex Morgan’s leaping header from Heather O'Reilly’s pinpoint cross pushed the United States to a 4-3 victory and a place in Thursday’s gold-medal game against Japan. But that play, which kept the Americans from the dreaded penalty shootout, was only the final twist in a game that was captivating, controversial, and compelling.
The Americans had talked about this game for months. Ever since the World Cup final a year ago, when they were upset in a penalty shootout by Japan, they targeted the London Games as their opportunity for payback. Now, they will have that chance as they get a rematch after the Japanese defeated France, 2-1, in London.
Canada showed little fear despite their lack of success against the Americans. The Canadians frequently battered the US players early on, mixing tough tackles with hard fouls. Megan Rapinoe was crunched more than once; Abby Wambach and Morgan, too.
The US players returned in kind, but the more compelling back-and-forth was the one waged on the scoreboard late in the second half. Canada’s Christine Sinclair had opened the scoring with the first of her three goals in the 22d minute. After Rapinoe tied the game in the 55th minute with a surprising goal straight from a corner kick — an Olimpico goal at the Olympics in soccer parlance — the game exploded. Sinclair responded with her second goal just 12 minutes later, leaping to deliver a powerful header beyond Hope Solo’s fruitless dive.
Undeterred, Rapinoe answered with a stunning strike in the 70th minute, expertly controlling a cross at the top of the penalty area and blasting a shot in off the post to level the game again at 2-2. At that point, it seemed that the Americans might take control and push ahead.
But Canada — and Sinclair — answered again. It was another high ball and another header for Sinclair, the Canadian captain, and another helpless gaze from Solo as the ball flew past and Canada led again.
Then, six minutes later, came the sequence that simultaneously brought protestations and celebrations. Referee Christiana Pedersen awarded the US a curious indirect free kick near the top of the Canadian penalty area; it appeared that Pedersen might have called Canada’s goalkeeper for wasting time as she held the ball before punting. The ensuing shot glanced off a Canadian defender’s elbow, and the Americans were given a penalty kick.
The Canadian players were livid, and neither decision was clear-cut. Time-wasting is very rarely called, and the defender, Marie-Eve Nault, had her arm tucked in front of her to protect her face when the ball hit her. The Canadians shouted at Pedersen over and over, and Melissa Tancredi earned a yellow card for her dissent.
Wambach stepped to the penalty spot and buried her kick, tucking it in off the inside of the post to even the game, yet again, and send it toward its dramatic conclusion.
Canada coach John Herdman told the Associated Press ‘‘it felt like it was America and the referee against’’ his team and if ‘‘the United States were honest they’d know they got lucky.’’
In the other semifinal, the Japanese took a two-goal lead after first-half strikes by Yuki Ogimi and Mizuho Sakaguchi, but France made it interesting late on Eugenie le Sommer’s goal in the 75th.
France’s Elise Bussaglia had a chance to equalize a minute later, but the midfielder rolled her penalty kick wide of the right post.