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.
"Obviously we are pleased with such an entertaining game as the centennial game," said Klinsmann, who scored 47 goals in 108 games for his country and coached Germany to the 2006 World Cup semi-finals.
"Overall it was a good performance, we saw a lot of things we wanted to see. Having a player like Clint Dempsey on your team it is a privilege, he is one of the best players in U.S soccer history."
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 November 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, allowed to get free by Omar Gonzalez, 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, to the delight of the 47,359 crowd, 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 later.
But the U.S held on for a morale boosting win after their 4-2 loss to Belgium in Cleveland on Wednesday ahead of three World Cup qualifiers, starting with Jamaica in Kingston on Friday.
Germany, without key players from Champions League finalists Bayern Munich and Borussia Dortmund, beat Ecuador 4-2 in Florida on Wednesday but despite the loss, coach Joachim Low was pleased with the mini-tour.
"It was worth it in all respects. With main players missing for various reasons I think we chose the right squad, they were very motivated and enthusiastic and if you ask them they would say they learned an awful lot," said Klinsmann's former assistant.
"For me it was worthwhile because even though you know them as players from the Bundesliga, you don't know them as human beings and it was really good to get a feel for them, what makes them tick".
