In Mirko Slomka's first game in charge, the hosts put on a sparkling display, taking the lead three minutes before half-time thanks to Petr Jiracek's header.
Pierre-Michel Lasogga doubled the advantage on 58 minutes, before a 50-yard wonder-strike from Hakan Calhanoglu in stoppage-time put the seal on an emphatic Hamburg victory.
It was a bitter blow for Dortmund, who had come into the game on the back of four successive wins in all competitions and will now seek to regroup ahead of Tuesday's UEFA Champions League last 16 tie with Zenit.
Klopp was gracious following the loss, Dortmund's first since December 21.
"Congratulations to Hamburg for a well deserved victory," he said.
"We wanted to change everything at half-time. We changed the system and we were more lively.
"Hamburg fought, we also fought, but ultimately we have not done enough to bring something away here.
"It was a very modest game for us."
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