The hosts started relatively brightly, but found themselves behind after just 11 minutes when Toni Kroos’ corner picked out Thomas Muller unmarked inside the area and the Bayern Munich man side-footed beyond Julio Cesar.
Klose then doubled the Germans' lead, slotting home the rebound after Cesar had pushed away his initial effort, and his record 16th goal in the tournament - taking him ahead of Ronaldo - signalled an unthinkable capitulation for Luiz Felipe Scolari’s side.
Kroos hit a quick-fire double as he drilled a strike past Cesar with the outside of his boot following Philipp Lahm’s cut-back, before making it four after Sami Khedira’s unselfish pass capitalised on some lacklustre Brazilian defending.
Khedira then got in on the act himself when he guided Mesut Ozil’s pass into the bottom corner after David Luiz’s error typified an abject showing from Scolari’s men, who were booed off at the break.
Brazil looked to restore some pride in the second half as Oscar and substitute Paulinho were both denied by Manuel Neuer, while Muller was prevented from making it six as Cesar tipped his effort over the bar with a fine save.
Germany replaced Klose just before the hour mark and it was his replacement, Chelsea's Andre Schurrle, who added a sixth when he converted Lahm's low cross from inside the box with a simple tap-in.
Schurrle then added his second and Germany's seventh of the night with a smart finish off the underside of the crossbar. Oscar grabbed a late consolation goal but the final whistle soon sounded as Low's side reached the final for the first time since 2002.
The Germans will now go into Sunday's final at the Maracana to face Argentina or the Netherlands on the highest of highs.
With Brazil looking to take inspiration from their missing talisman, Neymar, the opening period was always going to be a testing one for Germany, with the partisan crowd baying every Brazilian touch and tackle.
Marcelo was cheered wildly after sending a 25-yard shot skimming a couple of yards wide, but there was a frantic feel to it, as though the Neymar emotion had spilled over into a frenzy, with Germany capable of punishing any slackness.
That almost happened early on when Ozil delivered a sweet cross for Khedira to volley only for his shot to strike Kroos.
A break by Khedira then led to the corner from which Germany took the lead in the 11th minute. Kroos took it, and it was straightforward enough but Brazil's marking went into meltdown and Muller slotted it home low past Cesar while Luiz beat the ground in frustration.
Marcelo burst into the Germany penalty area and a pinpoint sliding tackle by Lahm stopped him in full stride but Brazil's high tempo only served to make them vulnerable on the break and Germany made them pay again, this time Klose becoming a World Cup's record-breaker.
A delightful passing move saw Muller lay the ball off and although Cesar stopped his first effort, Klose buried the rebound.
Two minutes later and it was 3-0, Lahm's cross going all the way across the area for Kroos to slam home left-footed from 18 yards.
Another two minutes, another goal. From a goal-kick Fernandinho was robbed by Khedira who unselfishly played in Kroos for a virtual tap-in for 4-0.
By this time Brazil fans were in tears and a few leaving their seats, but the German machine marched on mercilessly.
Less than half an hour gone and the hosts were 5-0 down. Mats Hummels strode forward and Ozil, who had come alive in this match, set up Khedira for a first-time finish.
Neuer had been barely tested in the first half but only he prevented Brazil getting on the scoresheet, first defying Oscar and then Paulinho.
Cesar had to be at his best to tip over Muller's curling effort from 25 yards, but Germany were not to be denied and Lahm's penetrating cross was struck home by substitute Schurrle.
It was Chelsea midfielder Schurrle who piled on the agony, a breath-taking finish into the top corner after pulling down Muller's instinctive cross.
Ozil should have made it an embarrassing eight but slid wide when through on goal before Oscar's crisp finish in the last minute provided a glimmer of light in the darkness.