Man-of-the-match Toni Kroos and substitute Andre Schurrle netted braces, while Muller, Miroslav Klose and Sami Khedira got on the scoresheet in a record-breaking semi-final fixture at the Estadio Governador Magalhaes Pino in Belo Horizonte.
Muller opened the scoring in the 11th minute - his fifth of the tournament - before a stunning capitulation saw Brazil concede four goals in the space of seven minutes in the first half.
Veteran striker Klose scored during that period, tucking away his own rebound in the 23rd minute to net his 16th World Cup goal - eclipsing Ronaldo's (15) record.
Despite Brazil being unable to call upon suspended captain Thiago Silva and injured star striker Neymar, Muller did not see foresee such a lopsided victory, which condemned Luiz Felipe Scolari's men to their first defeat on home soil since 1975.
"This was not to be expected," the 24-year-old told reporters. "I don't know what to say to be honest.
"I can't believe it. It's something totally crazy. It just went well today.
"Now we have to pull through one more time, we have to fight to get this thing."
Germany - aiming to win their fourth World Cup and first since 1990 - will now face the winner of Wednesday's semi-final between Argentina and the Netherlands, though they do have an injury concern.
Central defender Mats Hummels, who injured his knee in Germany's 4-0 demolition of Portugal in the opening group game, was withdrawn at the half-time interval due to tendonitis on Tuesday.
Hummels was replaced by Per Mertesacker after feeling his comfort in his knee but the 25-year-old insisted his substitution was purely precautionary ahead of the decider at the Maracana on Sunday.
"Since a few days I had problems and I decided for me to go out, so it does not get worse," said Hummels.
"I'll treat me now and hope for a best on Sunday."
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