LONDON  — First-time Olympian Alex Morgan already has her defining moment: A game-winning goal in overtime that put the U.S. women’s soccer team into the gold medal match.

And of all things, it came on a header, the very skill that was supposed to be a weakness in her game.

If she keeps this up, she really will outgrow her nickname.

“We came up with the name ’Baby Horse’ a while back when she first came on the team,” U.S. midfielder Megan Rapinoe said Tuesday. “Just so much talent. Obviously very raw, she was kind of wild.

“And now she’s a beautiful stallion, I think.”

That sounds about right. The lightning-fast striker brings beautiful goals to game at the formative age of 23. Long after Abby Wambach, Christie Rampone and the other vets have retired, it’s a reasonable bet that Morgan will be the face of the U.S. national team.

“She’s still a genetic freak, in my opinion,” Wambach said. “She makes plays that you don’t expect anybody to make.”

When Morgan looped Heather O’Reilly’s cross into the net in the 123rd minute of Monday night’s 4-3 win over Canada in the semfinals, she set up one of the most tantalizing rematches of these Olympics: United States vs. Japan for the gold medal.

Japan beat the Americans in penalty kicks to win last year’s World Cup, back when Morgan was still a super-sub who came off the bench in the second half and created all sorts of havoc with her speed.

Now comes the chance to ease the sting of that defeat Thursday at Wembley Stadium. Morgan knew four years ago, when she was up in the wee hours of the morning watching the U.S. games on television during the Beijing Games, that she’d be a part of this group.

“At that moment, I knew I was going to be with this team at the next Olympics,” Morgan said.

She’s had that vision before, and was right.

“I’ve wanted to be a professional athlete since I was 5 years old,” she said. “I actually have a note in my mom’s office that I wrote when I was 5 that said ’When I grow up, I want to be a professional athlete.’ And she still has it to this day.”

Casual fans — not to mention some die-hard soccer fanatics — were asking why Morgan wasn’t starting when she was scoring goals at the World Cup, but coach Pia Sundhage said young striker didn’t yet have a complete game, not enough to play a full 90 minutes.

A strong performance at the Olympic qualifying tournament in January propelled Morgan into the lineup, and she’s justified the promotion by piling up goals and setting up Wambach during the run-up to London. The latest proof came in her game-winner, using the very technique her coach had told her wasn’t her thing earlier this year.

“How good will she be in four years?” Sundhage said. “Depends on what she wants.”

The goal against Canada was Morgan’s third of the Olympics and her team-high 20th in 2012, joining Mia Hamm (1998), Kristine Lilly (1999) and Wambach (2007) as the only U.S. players with 20 goals in a calendar year.

U.S. women’s soccer gets a lot of love during the World Cup and Olympics, but it often takes a long publicity hiatus after the Summer Games. It’ll be three years before the next World Cup, and it’s uncertain whether there will be yet another attempt to form a top-flight U.S. women’s league anytime soon.

A marketable player like Morgan can boost the sport’s profile during the down times, especially if the public has memories of game-winners on a march to the gold.

“I think maybe in the beginning people saw her as a pretty face who scores goals,” Rapinoe said. “But she’s so much more than that. Her game has developed so much.”