Germany took a 2-0 lead with goals in the first half through Miroslav Klose and Lukas Podolski before Matthew Upson reduced the deficit with a headed goal. The game was tighter at the start of the second half, before Germany finished it with two lethal counter-attacks that exposed England's aged, creaking defence.
The game's turning point came in the first half, when England should have gone in level after a Frank Lampard shot crossed the line coming down off the underside of the crossbar, only for the linesman to wave play on.
The irony was not lost on fans who remembered the controversial goal that Geoff Hurst scored in the 1966 World Cup final in London, when England won 4-2. Unlike Lampard's strike on Sunday, video evidence has never satisfactorily made clear whether Hurst's shot crossed the line.
Referee Jorge Larrionda's misjudgement was all the more inexplicable because he was well-placed to see the incident. Yet, after looking across at his linesman, he waved play on.
England coach Fabio Capello said that the Lampard moment changed the game. "The Lampard incident was one of the most important in the match," said Capello.
"The referee made one of the biggest mistakes, but Germany are a great team, we were caught out on the counter-attack. This is football. Little things make all the difference."
The controversy over the incident will rumble on but England will also have to ask themselves some hard questions after what was, at times, a shambolic display.
Needing to attack and pushing up the field in the second half, England's defence was shown up by two brilliant counter-attacking strikes from Thomas Müller, which finished off a struggling England.
Three-times champions Germany, whose speed and guile frequently bewildered a statuesque England backline, will now meet either Argentina or Mexico, who were facing off later Sunday in Johannesburg.
Lukas Podolski, who scored Germany's second goal, said after the match, "I think we deserved to win. Now we have to make sure we don't sit back like we did after the game against Australia."
Germany's instrumental midfielder Bastian Schweinsteiger said, "I'm really proud of the team. What we did over the 90 minutes was great. We were all pitching in at the back. Of course, we were lucky with Lampard's goal, but we played really well."
Criticizing his own team's performance after taking the lead, Schweinsteiger said, "We should never have let a two-goal lead slip like that."
Germany, a youthful side just coming to the boil under coach Joachim Löw, continue their record of having reached at least the last eight in every World Cup they have competed in since 1938.
"It was fun to watch," Löw said after the match. "We played with so much spark and vigour against a really experienced team."
England, having come to the tournament with high expectations under the experienced Capello, will head home with their reputations in shreds ahead of the customarily savage media post-mortem.