"We fight to the last second," Klinsmann said. "It was a grind but a wonderful win at the end of the day. There are undoubtedly things that we need to improve on. The U.S. team always has a great spirit."
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U.S. fans were screaming for revenge Monday after the Black Stars eliminated the Americans from the last two Cups.
They got it. At a price.
Clint Dempsey scored a shocking goal a half-minute in, but the U.S. couldn't make it stand up. Andre Ayew tied the score in the 82nd minute after a brilliant back-heel pass from Asamoah Gyan, who had eliminated the U.S. four years ago.
And then, just four minutes later, 20-year-old John Brooks rose to head in Graham Zusi's corner kick from eight yards -- the first substitute to ever score for the United States in 30 World Cup games over 84 years.
The defender, an unexpected addition to the American roster, was so overcome he fell to the field and was unable to move even after teammates climbed off the dog pile. He had made his national team debut only last August, and Brooks hadn't scored in four appearances.
"I told my teammates that I had a dream two days before that I scored. My dream came true," Brooks said.
Klinsmann said he put his faith in Brooks.
"We coaches always try to read the players coming into the youth system and how can this player be developed over time," Klinsmann said. "With John Brooks, his passing is amazing; he's calm for his age and strong in the air. And he rarely fouls. We had the feeling he's ready for the World Cup. We knew that if we had the time to work him through every training session, then he's willed to take that on quickly. Now we have to keep him consistent with his performance from today."
U.S. players ran onto the field to celebrate at the final whistle, jumping as supporters chanted "U-S-A! U-S-A!" Now the Americans are in good position in Group G, where Germany opened with a 4-0 rout of Cristiano Ronaldo and Portugal.
"It's what we expected," said Klinsmann. "We got the three points that we wanted and we can move on."
Klinsmann had said this would be like a final. Altidore was hoping it wasn't his finale.
The forward was carried off on a stretcher after his left hamstring gave out in the 21st minute when he tried to control a long ball. He awaits tests that will determine whether he can return for this World Cup.
Dempsey went down too on a balmy late-autumn night but stayed in the game. The U.S. captain ended the first half with a tissue up his nose to stop the bleeding after John Boye's kick to his face during a battle for a header in the 31st minute, and he was struggling for breath in the second.
Matt Besler came out at the start of the second half after feeling tightness in his right hamstring. It was his replacement, Brooks, who scored the winning goal. Zusi was also a sub, coming on for the hobbling Alejandro Bedoya in the second half.
By the time of the final whistle, the U.S. lineup had Brooks in central defense and a virtually invisible 23-year-old Aron Johannsson at forward.
Now the odds favor advancement. But that might depend on which players are able to make it on the field for Sunday's game against Portugal in the hot and humid Amazon rain forest capital of Manaus.
Dempsey's goal came on a low shot just 32 seconds into the match. The lead held until Ghana's Ayew leveled in the 82nd minute. Ayew's goal appeared to have stolen the victory from the U.S., until Brooks' goal off a corner from Zusi.
"It was a dream come true," Dempsey said. "We showed a lot of character. We have to do a better job at keeping possession and building out of the back. We have to stay sharp on set pieces. This win will give us confidence going into the next game. The boys showed a lot of heart. Our fitness showed."
Dempsey' goal made him the first U.S. player to score in three different World Cups and was the fastest ever scored by an American in the tournament. The U.S. is now tied with Germany atop of Group G.
Goalkeeper Tim Howard said he was concerned the team would have trouble keeping momentum after Dempsey's early goal.
"That game went just as planned," he said. "We took our chances well. Natural tendency when you score is to drop off, but we defended well."
Information from The Associated Press was used in this report.
Klinsmann: We have a great spirit
United States head coach Jurgen Klinsmann reflects on his team's fighting spirit to come away with the victory against Ghana.
Brooks stuns Ghana with go-ahead header
United States centre-back John Brooks scored a stunning header to give the United States the 2-1 lead over Ghana.
John Brooks (United States) Goal - Header at 86'
Goal! Ghana 1, USA 2. John Anthony Brooks (USA) header from the centre of the box to the high centre of the goal. Assisted by Graham Zusi with a cross following a corner.
GOAL: Ayew (82') Ghana 1-1 United States
2014 FIFA World Cup Group G: Andre Ayew (82') Ghana 1-1 United States
Andre Ayew (Ghana) Goal at 82'
Goal! Ghana 1, USA 1. Andr Ayew (Ghana) left footed shot from the centre of the box to the bottom left corner. Assisted by Asamoah Gyan.
Clint Dempsey (United States) Shot On Target at 79'
Attempt saved. Clint Dempsey (USA) left footed shot from outside the box is saved in the top left corner. Assisted by Fabian Johnson.
Jermaine Jones (United States) Shot On Target at 63'
Jermaine Jones (United States) Shot On Target at 63'
Asamoah Gyan (Ghana) Shot On Target at 58'
Attempt saved. Asamoah Gyan (Ghana) header from the centre of the box is saved in the top right corner. Assisted by Daniel Opare with a cross.
Sulley Muntari (Ghana) Shot Off Target at 55'
Attempt missed. Sulley Ali Muntari (Ghana) left footed shot from outside the box is close, but misses to the left. Assisted by Christian Atsu.
Dempsey gives U.S. first half lead
United States took an early lead via Clint Dempsey, but an injury to Jozy Altidore has ruled the striker out of the match.
Dempsey kicked in the face
U.S. captain Clint Dempsey had to receive treatment for a bloody nose after being kicked in the face by Ghana's John Boye.