Top-selling Bild devoted six of its eight main pages to the match under the banner headline "Speechless!", summing up the sense of disbelief at the scale of the win.
A picture of jubilant two-goal midfielder Toni Kroos adorned the front page. "Boys, you are immortal!" read the gleeful column in Bild, which thanked all the team by name and coach Joachim Loew.
"Germany will never forget this July 8, 2014... Thanks for this moment of glory. Thanks that we could experience it!"
The paper dedicated a full page to each of the five German goalscorers in their red and black strip.
Daily Die Welt's website - the victory was too late to make many papers' print editions - called the match "The Seventh Wonder of Football".
It ran a picture of striker Miroslav Klose, 36, who netted once to become the tournament's all-time leading scorer with 16 goals.
In a country where, largely for historical reasons, outbursts of national pride are rare, Germans did not hesitate to treasure the win.
Despite heavy storms, fireworks rang out across Berlin after each goal on Tuesday night and after the final whistle cars raced through the city with honking horns and German flags hanging from the windows.
Commentary filled the airwaves, with former players lining up to speculate on whether the squad is as good as the revered West German World Cup winning teams of 1954 and 1974. The Germans also won in 1990.
Germany hopes to go on to win its fourth World Cup in Sunday's final, which Chancellor Angela Merkel, who is regularly welcomed into the squad's dressing room, is expected to attend.
Looking ahead to that match, the online edition of the Sueddeutsche Zeitung wrote "Off to Rio on a High".
But some commentators tempered the celebrations with workmanlike reminders that the event that will define the team's legacy is still to come.
"If you win 7:1 you have done everything right," former national player Olaf Thon told Deutschlandfunk radio, adding the game would be remembered as a "game of the century". However, he cautioned not to take anything for granted: "But in the end what will count is who wins the final."
Germany will face either Argentina or the Netherlands, who play each other in the second semi-final on Wednesday.
(Reporting by Madeline Chambers; Editing by Stephen Brown and John Stonestreet)
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