It was a result the former Bundesliga champions badly needed.
They were on a run of three consecutive defeats, and another would have sent them crashing out of the competition in which they were last season’s beaten finalists.
It was a do-or-die situation for Klopp and his men, with their season lurching at the precipice of the abyss.
They now know that their fate is in their own hands, and that a win over Marseille in their last group stage match will book their ticket into the last-16.
"We want to continue living our Champions League dream despite all the prophecies of doom," a relieved Klopp told reporters after last night’s match.
"It all looks better now but we still need to win in Marseille."
Dortmund’s determination to turn their season around was personified by Sven Bender.
Deployed as an emergency defender due to his team’s injury crisis, Bender played the game with a broken nose.
"It was a great game for him and we had to change his bloodied shirt several times. The last one we got from the club shop," Klopp said admiringly.
With three points in the bag against tricky Napoli, Dortmund can now relax a little ahead of their clash against Marseille.
But Klopp already has his players on their toes, readying them for another last-ditch fight for their Champions League survival.
"Our chances are much better than before the game but nothing has been settled yet," he said.
"Thinking that we are already through would be a big mistake but it is now in our hands to stay in the Champions League."