Germany did not need any miracles on this occasion. Sixty years to the day since the old West Germany fashioned the Wonder of Berne to beat Hungary in the final of the 1954 World Cup, Joachim Löw’s current crop produced a performance of cool authority to edge one step closer to glory.

This was a long way from being another thriller at this tournament of thrilling matches and the narrative was shaped instead by traditional German virtues, chief among them control, discipline and that age-old tournament know-how. As Didier Deschamps, the France manager, noted afterwards, Germany have vast experience of these high-stress knockout ties. They made it count here.

Germany scored early and there was never the sense that they would relinquish their grip. The conviction ran throughout the team, from the imperious goalkeeper, Manuel Neuer, to the captain, Philipp Lahm, the centre-half Mats Hummels and the attacking midfielder, Thomas Müller.

France created chances and a couple of them stuck in the memory – Mathieu Valbuena’s 34th-minute shot and Karim Benzema’s injury-time effort, both of which extended Neuer. But they failed to muster any sustained periods of pressure and they even looked a little intimidated. Deschamps admitted that they had started in “timid” fashion.

For France, there would be no revenge for the semi-final defeats against Germany at the 1982 and 1986 World Cups and, if the regrets took in the lack of ruthlessness up front, they centred upon the moment when the defender Raphaël Varane did not do enough to prevent Hummels from heading the only goal. It was perhaps fitting that a defender should make the difference. Hummels deserved to be named as the man of the match.

“We are playing the kind of football that gives us a chance to win the World Cup,” Hummels said. “You cannot always score two more goals than your opponent so you have to defend properly. This wasn’t a walk in the park or the perfect match. But if we can carry on, a few things can pan out.”

Löw made tactical changes and nobody could say that they did not work out. He moved Lahm to right-back and Müller to the right wing, where they combined effectively while Miroslav Klose, recalled at centre-forward, chased wide to harry the France full-backs. In central defence, Per Mertesacker paid for his lack of pace with his place. “Per had a marvellous reaction when I told him,” Löw said. “He said, I know how I can help the team.”

The goal owed everything to the power of Hummels, which was clearly back at its maximum after the fever that had ruled him out of the last-16 tie against Algeria. From Toni Kroos’s whipped free-kick, he extended his arm to fend off Varane and guided the header beyond Hugo Lloris. It bounced down and in off the underside of the crossbar, before rearing up into the roof of the net for added emphasis.

Varane had to be stronger. Then again, Hummels and this Germany team are formidable, even in such heat. The 90 per cent humidity brought back memories of the semi-final between the countries at Mexico ’86 and it was a test of endurance, as much as anything else. “It was so hot you could hardly breathe,” Löw said. “At least our semi-final will be at 5pm [local time] when the sun is lower.”

The pattern was entrenched from the early running; Germany hogging possession, their movement and short passing sharp, looking to wear down their opponents and France snapping on the counter, seeking to profit from direct balls.

Germany’s defensive line was not as high as it had been against Algeria, which meant that Neuer did not need to charge out of his goal, but France did get in behind them at times. The pick of their chances fell to Valbuena after Antoine Griezmann’s wonderful driven cross but Neuer denied him smartly and Hummels blocked Benzema’s rebound effort.

Benzema had earlier dragged a volley wide following Valbuena’s incision while the striker had further sightings of goal in the first half. He lost Hummels from Patrice Evra’s cross only to head at Hummels and also shot at Neuer. At the other end, Klose fell theatrically inside the area but Mathieu Debuchy did tug at his shirt.

Germany sought to close the game out in the second half, to stay compact and tick off little blocks of time. They would have enjoyed a more comfortable finish had André Schürrle, who came on for Klose, been able to finish either of his glorious counter-attacking opportunities.

The first was created by Mesut Özil, who otherwise struggled and looked non-plussed when he was substituted. Özil’s cross was missed by Müller but Schürrle looked the favourite to convert behind him. Lloris saved. Towards the very end, from Müller’s cross, Schürrle was denied by a brave block from Varane.

Deschamps introduced Loic Rémy for Yohan Cabaye and his team did press on to the front foot a little more in the second half. The full-backs got forward on the overlap and there was the scent of an equaliser. Benzema was denied by another Hummels block and Blaise Matuidi had a shot saved by Neuer. When the goalkeeper beat Benzema’s last-gasp effort away with a mighty glove, France were staring at the exit.

“I’m disappointed, frustrated but let’s not forget what we have done so far,” Deschamps said. “I don’t think there was a huge gap between the teams. They are more experienced and we were timid at the beginning but we created some chances. We were not efficient and Neuer played well, too. I’m proud of my players and my staff and that’s what I told them at the end.”