A penalty awarded seconds before half-time caused turmoil in the German camp. Griezmann took his chance and added a second strike to extend his lead as the tournament's leading scorer and become France's new football hero.
"He's our little Mr Extra," said fellow striker Olivier Giroud after the dramatic win before 65,000 spectators on a hot Thursday night in Marseille.
France's first victory over their rivals in a major tournament since 1958 came out of a controversial penalty decision at the end of the first half.
The 2014 World Cup winners had dominated possession and German coach Joachim Loew said he had to "calm the players down" in the dressing room at half-time because of the penalty.
Germany renewed their control of the ball in the second half but Griezmann rattled them again with a 72nd minute goal.
Paul Pogba's cross from the left was cleared by Neuer into the Atletico Madrid star's path to fire home through the legs of the goalkeeper who had only conceded one other goal in regulation time at the tournament.
Sunday's final will pit Griezmann against Ronaldo and a team from a nation of 11 million people against one of Europe's giants, who won the World Cup in 1998 at the same venue and the European title in 1984.
French coach Didier Deschamps hailed Germany as a "a great team."
"We found it tough but we didn't give up," he said praising his own players' determination.
France's recent years have been clouded by defeats and scandal, including a player strike at the 2010 World Cup. Now the country appears to be behind them again.
nine scored in one tournament by French legend Michel Platini in 1984. He was particularly relieved to have scored the penalty, having missed one when Atletico Madrid played in the Champions League final against Ronaldo's Real Madrid in May.
"I wanted to take a penalty again in an important moment and I'm happy I did, and happy I scored," he said.
"For the second goal I was hanging back to wait for an error from the goalkeeper. I am happy with the goals but I am still a long way from Platini," said Griezmann who was rejected as too small by French clubs and made his name in Spain.
Evra said the team had been told so many stories about the last time France beat Germany in a major tournament, at the 1958 World Cup. The psychological barrier was broken with victory in the November 13 friendly which was soon forgotten when suicide bombers detonated explosives outside the Stade de France at the start of a series of deadly attacks in Paris.
"As soon as we beat them in a friendly, it gave us a lift," Evra said.
German coach Loew said his team had been the better of the two. Goalkeeper Neuer said the result was undeserved.
"We have played well at these European Championship finals, but we're out. That's very bitter," said Neuer.
"It's a semi-final and there is not a more stupid moment (to go out) and it's not a fair result."
Loew refused to say whether he would extend his time as Germany's manager beyond the campaign for the 2018 World Cup in Russia.
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