By FOX Sports staff
Defending champions Dortmund looked on track for all three points at the BayArena after racing to a 2-0 lead inside nine minutes thanks to strikes from Marco Reus and Jakub Blaszczykowski.
However, Stefan Reinartz reduced the deficit in the 58th minute before pulling the hosts level with his second five minutes later, but Robert Lewandowski netted what proved to be the winner seconds later to help his side leapfrog Leverkusen into second place.
Given the way the match unfolded, Klopp believes his side were deserving winners even though there was a touch of luck in the manner of their victory.
"The two teams forced each other to make mistakes," he said on the club's official website. "The game saw a lot of twists and turns.
"What we learned today [Sunday] is that there are not too many teams that can win here. We knew at half-time that the game wasn't even close to being over.
"Our win was fortunate, but not undeserved."
The 45-year-old also praised his side for the way they came back to grab the winner after seeing their two-goal lead cancelled out by Reinartz's quickfire brace.
"We wanted to change our system earlier but [Ilkay] Gundogan's injury prevented us from doing so," Klopp revealed. "At that stage Leverkusen scored their first goal.
"We came back after the equaliser and had a chance to make it 4-2. That's great character.
"We can defend much better than we did today [Sunday], but I'm not sure if this was because of our errors or because of the opposition's quality."
Despite overtaking Leverkusen, BVB remain 12 points behind leaders Bayern Munich and face an uphill task in their bid to retain the league title.