Dempsey's second half double provided the Americans with a commanding 4-1 lead before Germany responded with two late strikes in a seven-goal international at RFK Stadium in Washington DC.
The Americans, celebrating the centenary of the U.S. Soccer Federation, had grabbed the lead in the 13th minute thanks to a powerful volley from Jozy Altidore, his first goal for his country since Nov. 2011.
Four minutes later, the advantage was doubled via an appalling error by German keeper Marc-Andre ter Stegen, who somehow allowed a routine back pass from Benedikt Hoewedes slip off his foot into the net.
Germany rebounded strongly after the half-time break, pulling one back in the 51st minute when Heiko Westermann powered in a header from a Max Kruse corner.
Two superbly finished goals from Dempsey, the second a beautiful curling effort from 25 yards, gave the U.S. a three-goal lead before the Germans began to pile on the pressure.
Kruse was given time to turn and shoot on the edge of the area in the 78th minute before Julian Draxler scored three minutes.
The U.S. held on for a morale boosting win after their 4-2 loss to Belgium in Cleveland on Wednesday ahead of three upcoming World Cup qualifiers.
(Reporting By Simon Evans; editing by Julian Linden)
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