Miroslav Klose struck twice in the opening 15 minutes before defender Per Mertesacker made it 3-0 in a game watched by German Chancellor Angela Merkel and Sweden's Prime Minister Fredrik Reinfeldt.
Klose's goals were his 66th and 67th in international football, taking him within one strike of the country's all-time leading scorer Gerd Muller.
Mikael Lustig pulled another goal back before Johan Elmander cut Germany's lead to 4-3 in the 76th minute, hitting in a shot between defender Holger Badstuber's legs.
"I feel a lot of pride for what the players have done here," Sweden coach Erik Hamren told the Kanal 5 television channel.
"Did we believe we could get a result at 3-0 down at halftime? No, no, there was no one who thought that."
"We played a different way in the second half," said the striker.
"We were too scared and had too much respect in the first half. After my first goal I felt they were backing off more and more."
"If you lead 4-0 and it ends 4-4 then something has definitely gone wrong," said captain Phillip Lahm.
"After Sweden's first two goals everything collapsed. That should not happen to a top team.
"We seemed to think we were done after leading 4-0. But we made too many mistakes and did not concentrate," added defender Lahm.
