Pierre-Emerick Aubameyang scored twice inside 20 minutes and Marco Reus added a third with a stunning long-range effort shortly before half-time to put Dortmund into a 3-0 interval lead in the Group D encounter.
There were noticeably fewer chances in the second half but substitute Adrian Ramos added a late fourth just a minute after entering play to complete the scoring at the Turk Telecom Arena and leave Dortmund just one win away from the knockout stages.
"The early goals have done us good," Dortmund coach Klopp told reporters. "It was a very intense game, but I will not break out now into euphoria.
"Today we could play our game and let our opponents come at us. Above all, we defended with great concentration."
The only sour note for Dortmund came when Sven Bender had to be replaced by Matthias Ginter with Klopp confirming the midfielder may have dislocated his elbow, while suggesting Shinji Kagawa and Mats Hummels both exited play with thigh complaints.
Dortmund's 100 per cent winning record in the Europe is in stark contrast to their poor Bundesliga form that has seen them lose five of their opening eight league matches.
Centre-back Hummels believes that Dortmund's victory was a result of their potency on the counter-attack, something he feels has counted against them domestically.
"We played with a lot of concentration, had no problems in defence and our fast breaks were very dangerous," he said,
"Besides that we were very effective, two chances, two goals [early on]. This is what our opponents did in the last few Bundesliga matches."
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