The game in front of 57,000 fans in Hamburg's Volksparkstadion started 15 minutes late due to heavy traffic and long queues for increased security checks following the attacks that left 130 dead and hundreds injured in the French capital last week.
Germany had played France last Friday in Paris and the players spent the night inside the stadium before being whisked off to the airport.
The friendly against Netherlands scheduled for Hanover on Tuesday, with Chancellor Angela Merkel set to attend, was then called off only two hours before the start.
The game in Hamburg started with a minute silence for the victims in Paris as well as another for the former West German Chancellor Helmut Schmidt who died on November 10, with fans holding French flags and messages of support.
Dortmund, attempting to close in on leaders Bayern Munich who take on Schalke 04 on Saturday, quickly lifted spirits with an attacking game but were twice caught on the break, with defender Mats Hummels heading in an own goal to complete a disappointing evening for them.
Ivo Ilicevic had a golden chance in the 16th minute only to fire desperately wide but the Croatian made amends, latching on to a superb through ball from Lewis Holtby and forcing keeper Roman Buerki to bring him down. Pierre-Michel Lasogga drilled in the 19th minute penalty.
Dortmund, with Marco Reus back from injury, again dominated but were once more caught off guard with a quick counter attack and Holtby slotting in from a tight angle three minutes from halftime.
The visitors came out battling after the break with Pierre-Emerick Aubameyang spilling a big chance wide and Dortmund shooting four times on goal in four minutes before Hummels turned a lone Hamburg cross into his own net to end any hopes of a comeback.
Aubameyang clinched a late goal to take his season tally to 14 but could not avert their second league loss of the season.
Dortmund remain on 29 points, five behind leaders Bayern with Hamburg, who needed a relegation playoff to stay up last season, move up to eighth with their second win in seven matches.
(Reporting by Karolos Grohmann, editing by Alan Baldwin)
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