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“He’s at the top of his form,” coach Vicente del Bosque said. “He’s first to the ball every time. Villa had that hunger for the goal that allowed him to convert.”

That goal came off the kind of attack that has carried Spain toward the top of the soccer world. Andres Iniesta surged through the Paraguay defense and passed to the right to Pedro, whose right-footed kick slammed off the goalpost.

The rebound came to Silva, and his shot hit the far post, then — amazingly — caromed across the net, off the left post and in.

Fans for both teams wore red and blended into the color scheme of the seats in Ellis Park Stadium. Even if you couldn’t see them so well, you sure could hear their vuvuzelas blaring, especially when Silva scored.

But Paraguay, a nation that never has been a factor at the World Cup and hasn’t won a major title since Copa America in 1979, wasn’t about to fold. The final six minutes of regulation and three minutes of extra time featured free-flowing soccer at both ends, and Casillas once again had to rescue the Spaniards.

Lucas Barrios broke free on right wing and Casillas charged out of his net to stop his hard drive. The rebound went to Roque Santa Cruz, and Casillas scrambled back to make a spectacular stop to preserve victory.

“Then Casillas, he was extraordinary,” del Bosque said. “Two magnificent stops there.”

At the end, as the Spanish players rushed to mob Casillas, a distraught Cardozo walked away from teammates and team officials, holding his jersey over his face, wiping away tears.

A tournament that belonged to South America for two rounds now has only Uruguay remaining from that continent after Brazil and Argentina also lost in the quarterfinals.

With the likes of Villa, Xavi, Iniesta, Xabi Alonso, Ramos and Fabregas, Spain’s game flows the way Brazil and Argentina have been known to do. It will need all of its creativity and a lot more precision against the Germans, who have scored four goals in three matches and routed England and Argentina in their last two games.

“The Germans have played a brilliant World Cup so far,” Iniesta said. “We’re also at the top of our game, I think. It will be a game between two rivals who enjoy having the ball and I think it will be a beautiful battle.”

Paraguay’s players couldn’t have been more relaxed before the game, smiling and waving to TV cameras as they came off their bus, then talking on cell phones and joking around on the pitch 90 minutes before kickoff.

The Spaniards were more matter-of-fact, in direct contrast to their playing style. They gathered in a circle and chatted, only occasionally giving a wave to their fans as the stadium began to fill.

But they gave them a huge thrill at the end, thanks to Villa and Casillas.