Khedira scored with a header in the 82nd minute for his first international goal after the Uruguay defense failed to clear a corner from Mesut Oezil. The goal ended Uruguay’s hopes of beating Germany for the first time in 82 years, while the Germans finished in the top three for the 11th time.

“We had hoped for more, and we did everything for it,” Khedira said. “This was some kind of final and we did everything for it. We have a young team and set an exclamation mark here and can reach more.”

Diego Forlan hit the crossbar with the last kick of the match in injury time, a free kick from the edge of the area.

“Obviously it’s something spectacular to be among the top four,” Forlan said. “If someone would’ve asked us at the beginning, we would’ve liked it. It’s something positive.”

Uruguay had come from behind to lead 2-1 when Forlan volleyed in Egidio Arevalo’s 51st-minute cross for his fifth goal of the tournament. Germany defender Marcell Jansen leveled five minutes later with a header after goalkeeper Fernanando Muslera misjudged a cross.

Thomas Mueller gave Germany the lead in the 18th minute, his fifth goal at the World Cup, sweeping the ball home after Bastian Schweinsteiger’s swerving shot had been stopped by Muslera, who was at fault in Germany’s first two goals.

Edinson Cavani equalized for Uruguay in the 28th when he slid a shot past goalkeeper Hans-Joerg Butt.

Uruguay has beaten Germany only once in 10 matches, in 1928. Germany beat Uruguay in the third-place match in 1970 — the last time Uruguay reached the semifinals.

“I don’t think it’s too much vanity to think that if we improve a little we can aspire to certain prominence in future international tournaments,” Uruguay coach Oscar Tabarez said.

Mueller and Forlan are now even at five goals with David Villa of Spain and Wesley Sneijder of the Netherlands, both of whom can raise their total in Sunday’s final.

Germany’s young team was missing five regulars through injury and illness, including striker Miroslav Klose. Klose missed a chance to match or beat the World Cup scoring record of 15 goals, held by Brazil striker Ronaldo.

In an action-packed match, Butt had two good saves from Luis Suarez and Forlan after his team’s second goal. The 36-year-old veteran, who was third-choice goalkeeper in 2002, got his World Cup debut instead of regular Manuel Neuer.

Substitute striker Stefan Kiessling missed an open shot late in the match to make it a bigger victory for Germany.

In its last three World Cup tournaments, Germany was runner-up in 2002 and third in 2006 at home.

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Lineups:

Uruguay: Fernando Muslera, Diego Lugano, Diego Godin, Jorge Fucile, Edinson Cavani (Sebastian Abreu, 88), Luis Suarez, Diego Forlan, Diego Perez (Walter Gargano, 77), Maximiliano Pereira, Egidio Arevalo Rios, Martin Caceres.

Germany: Hans-Joerg Butt, Jerome Boateng, Arne Friedrich, Per Mertesacker, Dennis Aogo, Sami Khedira, Bastian Schweinsteiger, Marcell Jansen Toni Kroos, 81), Thomas Mueller, Mesut Oezil (Serdar Tasci, 90), Cacau (Stefan Kiessling, 73).