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Natal, Brazil • After Clint Dempsey's historic early goal, the United States spent more than an hour struggling to hold off wave after wave of Ghana attacks. It was no surprise when Ghana tied the game in the 82nd minute.

Once again, the Black Stars — who had eliminated the Americans at the past two World Cups — were poised to ruin the tournament for the U.S.

With two starters out with injuries, the U.S. barely threatened in the second half until a corner kick in the 86th minute. Graham Zusi lifted the ball into the penalty area, where fellow substitute John Brooks rose above the defense and headed in the game-winner, putting the U.S. atop the group with Germany.

"I couldn't believe it. ... I just ran in the box and hoped that the ball would hit my head and it did," said Brooks, a 6-foot-4 defender who is brought forward for set pieces.

"It's a special moment for the boy, he did well," Klinsmann said.

The loss put Ghana at the bottom of Group G with Portugal — the Americans' next opponent. The top two teams in the group advance.

At the final whistle, coach Jurgen Klinsmann, the German hired to transform the U.S. from mere World Cup participant into a potential power, threw his arms to the sky and roared.

"The U.S. team always has great spirit," Klinsmann said. "I said it to the bench minutes before we're going to get some chances still. So we are still in the game after the equalizer, we just need to kind of push and push and grind it out. That's what they did. Here comes a set piece we trained over and over and over that stuff. And [Brooks] puts it in, so well deserved."

The U.S. lost striker Jozy Altidore to an apparent left hamstring injury in the 21st minute and his status for the rest of the tournament wasn't immediately known. Dempsey had his nose bloodied with a knee to the face.

"I was coughing up blood a little bit. Hopefully I'll be able to breathe through my nose again before the next game," Dempsey said.

Dempsey's goal — 29 seconds into the game — made him the first U.S. player to score in three different World Cups and ranks as the fifth-quickest goal in World Cup history.

Real Salt Lake captain Kyle Beckerman started in his first World Cup appearance.

DaMarcus Beasley, who became the first American to play in four World Cups, started the buildup to Dempsey's goal with a pass to Jermaine Jones, who fed it to Dempsey inside the penalty area.

With a nifty move to split defenders John Boye and Sulley Muntari, Dempsey sent the left-footed shot past goalkeeper Adam Kwarasey, where the ball bounced off the post and in.

Ghana enjoyed 59 percent of the possession in the game. Ghana applied relentless pressure on U.S. goalkeeper Tim Howard and finally drew even when captain Asamoah Gyan flicked a backheel pass to Andre Ayew, who used the outside of his left foot for a powerful shot. —

U.S. wins Cup opener

• Clint Dempsey scores within the first minute of the match.

• Substitute John Brooks scores the winning goal on a header in the 86th minute.

• Star striker Jozy Altidore leaves after a hamstring strain.