His close range strike in Belo Horizonte on Tuesday put Germany 2-0 up in the last four clash and was his first goal in a World Cup semi-final.
"Miro is just incredible," said Germany coach Joachim Loew, who did not start Klose in the three group games or against Algeria but inserted him into the line-up as a substitute against Ghana. Klose was in starting XI against France and Brazil.
"That he was able to break this record against Brazil and in the host country is an incredible achievement for him. I'm really, really pleased for him."
Klose, 36, netted his first World Cup goal against Saudi Arabia in 2002. He has played in four World Cups and has now scored 71 goals in 136 appearances for Germany.
"I don't think I can really measure what that it all means just yet, it's difficult to think about that after a match like this," said Klose when asked about breaking the record.
"We had a really truly super start," he said. "We analyse the opponents really well. I've said all along how important set pieces are and Toni put the ball exactly where it belongs. That's a great strength we have. We need to keep working on it."
A lethal finisher, Klose is the best German striker of his generation.
He began his World Cup career in 2002 with five headed goals as Germany reached the final, where they lost 2-0 to Brazil with Ronaldo scoring twice to register eight for the tournament.
Four years later with Germany as hosts, Klose won the Golden Boot when he scored five goals in leading the team to the semi-finals. In 2010 he scored four goals in South Africa.
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