Mats Hummels headed the winner as Germany beat old rivals France 1-0 to advance to the World Cup semi-finals for a record fourth straight time on Friday.
Borussia Dortmund defender Hummels rose to head home Toni Kroos's free-kick on 13 minutes to settle a cagey encounter at Rio de Janeiro's Maracana Stadium.
Joachim Loew's side will now play the winner of Friday's second quarter-final between Brazil or Colombia in next Tuesday's semi-final in Belo Horizonte.
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.
In Friday's other quarter-final, Brazil will aim to banish their jittery second round performance against Chile when they face Colombia in Fortaleza.
Brazil coach Luiz Felipe Scolari believes the lack of bad blood between his side and Colombia will allow for an attractive spectacle when the two sides clash in their World Cup quarter-final.
Scolari's men needed penalties after a bruising 120 minutes to overcome Chile in the last 16 which left many of the Brazil squad in tears at the end of the match.
However, the 65-year-old is hoping a less frenetic encounter will allow his players to show their talent in Fortaleza.
"Colombia is a more technical team than Chile," said Scolari. "Chile have more strength and play with a spirit which makes the game dynamics very different. The rivalry with Colombia is not the same as with Chile, Argentina or Uruguay.
"It was much more difficult against Chile. Colombia are also a great team with some great players, but when we don't have these rivalries our players feel more at ease."
Brazil's star man Neymar said the sessions were having the desired effect.
"I had never done anything like it before and I am quite enjoying it," added the 22-year-old. "It is not only us, in football, who are surrounded by emotion every day and need psychologists. I think it could do every person good, to make one more relaxed."
Scolari is expected to stick by Fred and Hulk, but will be forced into at least one change from the side that faced Chile as Luis Gustavo is suspended.
Gustavo's absence is even more critical for the hosts given the sensational form of the tournament's top goalscorer, Colombia's James Rodriguez.
The Monaco playmaker has taken on the mantle of his side's focal point with ease in the absence of the injured Radamel Falcao with five goals in four games.
A fourth consecutive win for Jose Pekerman's men took them into the last eight for the first time and ahead of the biggest game in Colombian football's history, the Argentine coach insisted the need to keep their feet on the ground.
"For Colombia every game is a new challenge and a step up," said the Argentine on Thursday.
"Both Brazil and us cannot think about what has gone before.
"We need to play our own game as we have done up to now and try to impose our play on them. The key is not to believe there is a favourite."
History, though, is against the Colombians as they have only beaten Brazil twice in 25 previous meetings and only once in a competitive fixture at the 1991 Copa America.
Cesar; Alves, Silva, Luiz, Marcelo; Fernandinho, Paulinho; Hulk, Oscar, Neymar; Hulk, Oscar, Neymar; Fred
Ospina; Zuniga, Zapata, Yepes, Armero; Aguilar, Sanchez; Cuadrado, Rodriguez; Martinez, Gutierrez
Brazil should just edge one of the most engrossing contests of the summer with a 3-2 extra-time win.
Belgium face Argentina in Saturday's World Cup quarter-final buoyed by support from Kenya, the country of birth of striker Divock Origi's father.
"We are very proud as a family, he has gone a notch higher than all of us," Origi's uncle Austin Oduor, a Kenyan civil servant and former captain of the Kenyan national team, told AFP.
"He has proved his credentials as a player, not just in scoring, but has shown he is able to play a big role in the team," Odour added.
Teenager Origi scored the only goal after coming on as a substitute in Belgium's first round win over Russia to fire Belgium into the last 16.
They went on to beat the United States 2-1 to set up Saturday's quarter-final with Argentina.
Against the USA, the 19-year-old Origi had been brought into the side at Romelu Lukaku's expense after impressing as a substitute in all three of Belgium's Group H wins and he was denied within the opening minute by Howard's outstretched leg after racing onto Kevin de Bruyne's through ball.
"He has propelled Belgium to do well to reach the quarter-finals. He has proved to be an asset and has become an important part to Belgium's progress," said Oduor.
Many in Kenya might otherwise have cheered for Argentina, popular here for iconic players like Diego Maradona.
But the Kenyan connection has boosted support for the Belgian team. Origi was himself once possibly touted for a call-up into the Kenyan national team, the Harambee Stars.
He is the son of Mike Okoth, who played for Kenya between 1989 and 2003. Two uncles have played for Kenyan champions Tusker.
Oduor was also a member of the Gor Mahia team which won the now-defunct African Cup Winners Cup in 1987.
"He is being celebrated as the first player of Kenyan origin of to score at a World Cup," Kenya's Daily Nation wrote this week, praising his ability to "poach from inside, strike the ball from afar and is a willing runner."
His uncle — whose son Arnold Origi is goalkeeper for Norway topflight club Lillestrom — believes the youngster made a wise decision to play for Belgium instead of Kenya.
"The atmosphere he's operating in is conducive for him, he wouldn't have found it anywhere else," Odour added.
"The Belgium team has given him space to operate and he has exploited it to the full.
"As such he has even silenced his critics who were thinking he would only sit on the bench during the World Cup. There is a lot at stake for him."