Dortmund's preparations for the clash at Signal Iduna Park had hardly been ideal, having been thumped 4-0 by Liverpool in a friendly on Sunday at Anfield.
However, Klopp's men looked much sharper than Bayern and took the lead midway through the first half thanks to Henrikh Mkhitaryan's strike from the edge of the box.
That advantage was doubled shortly after the hour mark, Pierre-Emerick Aubameyang outjumping Jerome Boateng to head home Lukasz Piszczek's cross from the right as Dortmund sealed Supercup success over Bayern for the second year running.
Klopp was pleased with the way his side responded from Sunday's match and was satisfied at having claimed the first silverware of the season.
"We said we wanted to put the Liverpool game behind us and we did that," he said. "We defended much better.
"It was about winning a trophy and we managed to do that. We'll make a T-shirt out of this."
Aubameyang, who donned a Spiderman mask pulled from his sock in celebration of his goal, echoed Klopp's sentiments.
"We're delighted to have made this start to the season and to be in such rhythm," he said.
