Brazil defeated Colombia 2-1 and Germany beat France 1-0 in the World Cup quarter-finals on Friday to set up a heavyweight semi-final showdown.
An early goal from Brazil skipper Thiago Silva and a stunning free-kick from David Luiz was enough to give the World Cup hosts victory over Colombia in a niggly last eight meeting in Fortaleza.
Colombia's star James Rodriguez left the field in tears after his sixth goal of the tournament, an 80th-minute penalty, was not enough to prevent Brazil from advancing to Tuesday's semi-final in Belo Horizonte.
The victory came at a cost for Brazil, though, with captain Silva picking up a yellow card which will see him suspended for the clash with the Germans.
Star striker Neymar was also stretchered from the pitch late in the game, potentially creating a problem for Brazil coach Luiz Felipe Scolari.
Television station Globo reported that he had been taken to hospital to undergo tests.
Silva had earlier settled Brazilian nerves, punishing slack Colombian marking at a corner to tap home after only seven minutes.
Luiz struck an astonishing 69th-minute free-kick to put Brazil 2-0 up before Colombia fought back.
Rodriguez, the outstanding player of the tournament so far, scored a penalty to make it 2-1 after Brazilian goalkeeper Julio Cesar brought down Carlos Bacca.
But Colombia were unable to find the equaliser to force extra-time as Brazil advanced to the last four.
Brazil's semi-final will see them play Germany in a repeat of the 2002 World Cup final won 2-0 by the South Americans.
It will be only the second time Brazil has met Germany at a World Cup.
Germany reached the semi-finals for a record fourth straight time earlier Friday after a header from Mats Hummels helped beat France 1-0 at the Maracana Stadium in Rio de Janeiro.
Borussia Dortmund defender Hummels rose to head home Toni Kroos's free-kick on 13 minutes to settle a cagey encounter.
"The next dream has come true," said man-of-the-match Hummels. "It's unbelievable that it's all going so well for us here at the World Cup.
"I hope that our journey won't end soon and that we can make it back to compete here week next Sunday," he added, referring to the July 13 final.
France coach Didier Deschamps bemoaned his team's failure to capitalise on the handful of chances they created.
"There was not much between the sides," Deschamps said.
"One team is more used to these occasions and has more experience.
"We were not clinical in front of goal." France had entered the match quietly confident of avenging semi-final defeats against Germany in 1982 and 1986.
But they were left to rue a lacklustre first half performance which saw Germany dominate in sweltering conditions.
France rallied in the second half and Hummels saved Germany with a desperate late block of a Karim Benzema shot shortly before Manuel Neuer parried a firm strike from Blaise Matuidi.
Andre Schuerrle should have sealed victory in the closing minutes, but with the goal gaping, struck his shot from Mesut Ozil's low cross directly at Hugo Lloris in the French goal.
There was still time for Neuer to save Germany at the death, pulling off a brilliant block from Benzema just seconds from the final whistle.
The quarter-final drama continues Saturday when the Netherlands play Costa Rica and Belgium take on Argentina.