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.

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

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.

Dempsey’s goal 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.

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.

The Black Stars regrouped at halftime, and the U.S. looked punchless on the attack. 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.

Ghana was still pressing when Brooks scored. The 21-year-old who plays for Hertha Berlin in the Bundesliga, appeared shocked, raising his hands to his head before falling to the ground to be mobbed by his teammates.