The champions were forced to dig deep for the three points after going a goal down early on, and their boss was enthused by the resolve they showed at his former ground
The 45-year-old's former side took an early lead through Marco Caligiuri, but die Schwarzgelben's first-half strikes from Marco Reus and Robert Lewandowski ensured the visitors made it four straight wins in all competitions.
Speaking after the match, the coach spoke of his enjoyment at being involved in such a testing encounter, but was ultimately relieved to have returned to Signal Iduna Park with all three points.
"This was an incredibly intense game," Klopp told reporters at the Coface Arena after the match. "Caligiuri's heroics were impressive, but we were then extremely clinical.
"We made a really good football match out of it. This was a test of our mettle and we passed it."
Dortmund's win has left the reigning Bundesliga champions second in the table after 13 matches, but still nine points behind runaway leaders Bayern Munich, who have only dropped five points domestically this season so far.