A dominant performance was not rewarded until 12 minutes from time, when Pierre-Emerick Aubameyang slotted home the opener following a defensive error.
Henrikh Mkhitaryan added a second just a minute later, before young goalkeeper Timon Wellenreuther was caught in possession by Marco Reus, allowing the Germany international to roll the ball into an empty net.
The result extends Dortmund's winning streak in the Bundesliga to four games and leaves them eight points outside of the Champions League places.
"It was an absolutely perfect afternoon and a really great game for my team," Klopp told Dortmund's official website.
"From the first to the last minute we looked good with the ball, moving into the right places and showed outstanding counter-attacking pressing.
"In the first half we had plenty of chances, but unfortunately we couldn't convert them.
"It was important for us not to show any nerves and we finally made a breakthrough after 77 minutes."
While there was no shortage of impressive individual performances from his team, Klopp was particularly keen to praise the contribution of Armenian playmaker Mkhitaryan.
He added: "I think that everyone wanted to jump on him when he scored. He had a really great game.
"It was the best game I've seen him play for Borussia Dortmund."
However, despite the euphoria of a derby victory, Klopp insists there is still plenty of work to do for his team.
"When I look at the table, we are still only five points clear [of the relegation zone], even though we have won four games in a row," he continued.
"This shows what kind of situation we were in and where we still are. We must not let up now."
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