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Germany will face Greece, which rallied to beat France 67-66 on a 3-pointer by Dimitrios Diamantidis. The win sends Greece into its first tournament final since 1989.
Greece won its only European title at home in 1987, while Germany was the 1993 champion.
"Tomorrow will be the most important game in my life," said Nowitzki, who plays for the Dallas Mavericks.
Nowitzki finished with 27 points and seven rebounds, going 5-for-10 from 3-point range. No other German scored in double figures.
Jose Calderon, who will play for the Toronto Raptors next season, missed a 3-point attempt for Spain at the buzzer.
"I've never seen the ball travel so long in my life," Nowitzki said.
Juan Carlos Navarro, who scored Spain's last 10 points, also finished with 27.
Germany blew a late 11-point lead when Navarro brought his team within one with 48 seconds left. German guard Pascal Roller turned the ball over and Navarro put his team ahead 73-72 with 14 seconds left on the clock.
But Nowitzki got free and made the winning jumper.
"We showed good nerves in the last seconds of the game, which we could have finished off much earlier," Nowitzki said.
Tony Parker, point guard for the NBA champion San Antonio Spurs, hit a 3-pointer to put France up 58-51 with 1:12 left. But he also missed two free throws with 38 seconds left, then turned the ball over with a bad pass.
Center Lazaros Papadopoulos dunked the ball to cut France's lead to 62-60.
Parker then made two free throws, but Theodoros Papaloukas made it a two-point game again. Rigaudeau made one of two free throws and after a quick French foul, Papaloukas made both for a 65-64 lead.
With 11.6 seconds left, Rigaudeau made one of two free throws before Diamantidis hit the winning shot.
Papadopoulos led Greece with 15 points and Dimosthenis Ntikoudis added 14 points and 11 rebounds.
Parker had 20 points for France and Boris Diaw added 14.
"We made some tactical mistakes in the last few seconds," Parker said. "But overall, I am happy with how we played. That's basketball, you win some, you lose some. We should have finished them off earlier."
Earlier, Slovenia qualified for the World Championship for the first time when it beat Croatia 89-80 in a consolation match.
The victory sent Slovenia into a playoff for fifth place against
Lithuania. Both teams have qualified for next year's World
Championship in Japan, along with the four semifinalists.