Hosts Brazil and Europe's biggest remaining team Germany set up an epic-looking World Cup semi-final for next week with deserved victories on Friday over Colombia and France respectively.
Five-times champions Brazil won a frenetic match in Fortaleza 2-1 to end Colombia's dream run to their first quarter-final, while France succumbed 1-0 to their old nemesis Germany in a more subdued affair in Rio de Janeiro.
Brazil and Germany will now meet in Belo Horizonte on Tuesday in a clash of styles and continents that is sure to excite fans around the world.
In a passionate and physical game from start to finish, Brazil captain Thiago Silva bundled in Neymar's corner with his waist after seven minutes to settle his nervy team mates.
Then a pumped-up David Luiz scored with a sublime 69th minute free kick to put Brazil two goals ahead.
Colombia's man-of-the-moment James Rodriguez pulled his side back into the match from the penalty spot, and got his sixth goal of the tournament, with just over 10 minutes remaining.
But Brazil's passion and will saw them hold firm.
"It was a great match, both teams played beautiful football," said the emotional Luiz, who prayed on the pitch and hugged Rodriguez in consolation at the end.
"It will be a big game (against Germany), a classic in world terms, and it will be very hard."
Rodriguez, the target of rough treatment from the Brazilians, wept distraughtly at the end. But he will long be remembered as one of the great players of this World Cup.
"We wanted to carry on, but we hold our heads high. Thank you Colombia," he said. "We're sad but we also have to feel proud because we left our skins out there."
Predictably, Brazil came to a standstill during the game, with businesses closed and cans rattling in empty streets as locals packed into homes, bars and beachside fanzones.
The final whistle signaled a cacophony of parties, fireworks and celebrations in a nation whose people believe they are destined to win a sixth World Cup on home soil.
The joy, though, was tempered by worries over Neymar, who was carried off on a stretcher after being kneed in the back, and the suspension of Thiago Silva for the Germany game after a yellow card for a needless foul on goalkeeper David Ospina.
HUMMELS GERMANY'S HERO
In the earlier quarter-final, defender Mats Hummels shook off the effects of flu and fever to win a surprisingly subdued match between the two European powers with a well-steered 13th minute header from a free kick. It gave Germany a remarkable fourth successive World Cup semi-final spot.
"I hope our ride isn't over yet and I hope we'll be back here," the 25-year-old Hummels said, referring to the July 13 final, also at Rio de Janeiro's Maracana stadium
He brushed off a challenge from France's Raphael Varane, appearing to push him lightly, to meet the ball perfectly before wheeling away in delight after securing a dream early lead.
Though perennially competitive, the Germans have not won soccer's ultimate crown since 1990 despite having a bigger pool talent since the unification of West and East.
'Les Bleus' looked uninspired but did have their moments, not least a stinging last-gasp shot by striker Karim Benzema that goalkeeper Manuel Neuer stopped one-handed. "That was just an automatic reaction," said the modest Neuer.
In truth, Germany, whose team showed no ill effects of a flu virus menacing their camp in recent days, never looked in great danger of losing and substitute Andre Schuerrle wasted two chances to secure a more flattering scoreline.
Though losing once more to old rivals Germany was painful, France have at least restored some pride after the embarrassment of in-fighting and a first round exit in 2010.
"We had our chances. But they had more experience than we did. They had us under control," said coach Didier Deschamps.
HELP FOR SUAREZ?
Away from the action, disgraced Uruguay striker Luis Suarez received a second offer to continue playing soccer during his four-month ban for biting an Italy defender at the World Cup.
Nart FC, a club in the self-declared Republic of Abkhazia within Georgia, said Suarez could join them and keep match fit because the local federation is not part of FIFA.
"Of course, we cannot offer the Uruguayan footballer a financial package that he is used to, but the Abkhazian championship is at its peak," said club president Gennady Tsvinariya.
Hajvalia from Kosovo have also offered the Liverpool striker - reportedly in talks over a possible transfer to Barcelona - the chance to play for them. The Kosovo Football Federation is also not a member of soccer's world governing body.
Back in Brazil, a second person was pulled dead from the wreckage of a collapsed highway overpass that was still under construction in host city Belo Horizonte. The accident on Thursday has revived concerns over rushed infrastructure.
Angry onlookers have been shouting anti-government slogans at the rescue site, saying local authorities and construction workers had cut corners because of the World Cup.
In the remaining two quarter-finals on Saturday, Europe squares off against Latin America.
First, Lionel Messi-led Argentina take on dark horses Belgium in a match that is hard to predict. Both teams have won four games from four, but curiously every win was by a single-goal margin, and neither have yet sparkled as expected.
In Saturday's second game, the Netherlands are hot favorites to end underdogs Costa Rica's dream run, but will have to guard against complacency given the Central Americans' extraordinary campaign, including wins over Italy and Uruguay.