Having fallen behind to a fine Elkin Soto goal in the opening minute following a mistake by Neven Subotic and Roman Weidenfeller, Dortmund launched a stirring fightback after half-time.
Goals from Subotic, Marco Reus, Pierre-Emerick Aubameyang and Nuri Sahin secured a win that lifts Dortmund out of the relegation play-off place and four points clear of the bottom two.
Klopp hopes the victory can be a turning point in Dortmund's season, after a disastrous first half of the campaign that has left them firmly in a relegation battle.
"We deserved to win," said the head coach. "This was a six-point game, but the severity of our task is unaffected.
"The first goal was slapstick, it was a terrible start. But we have responded very well.
"We knew we would create the chances if we continued to play and stay on track. We have scored great goals, [so] all is well."
