The reigning German champion had a field day against the Billy Goats, whose awful defensive performance resulted in a memorable rout at their own stadium
Milivoje Novakovic opened the scoring to give the Billy Goats in the first half, but Jurgen Klopp's men drew the game level before halftime through Lukasz Piszczek.
After the break Dortmund hit the hosts with a brace from Shinji Kagawa and strikes from Ilkay Gundogan, Robert Lewandowski and Ivan Perisic to seal an impressive victory.
The reigning German champion started the game hesitantly, misplacing passes and losing possession in dangerous areas. In 13th minute, however, it was given a rude awakening as its lethargic approach finally backfired.
A cross from the right by Martin Lanig caught Borussia Dortmund unprepared as Novakovic slipped away from Neven Subotic before sending a looping header over the badly positioned Roman Weidenfeller to give the Billy Goats the lead.
BVB tried to produce an immediate answer, but was struggling to create chances from open play in front of Michael Rensing. It came as no surprise, though, that the equalizer for Dortmund came from a set piece, which Koln utterly failed to deal with.
In the 26th minute Marcel Schmelzer picked out Piszczek with a sumptuous cross, and the Poland international applied a skillful header to beat Rensing and draw the game level. The goal acted as a catalyst for Dortmund, which had the upper hand for the rest of the period.
In a rare Koln attack, however, Lukas Podolski had a chance to restore the Billy Goats' lead in the 38th minute as he was released in a one-on-one with Weidenfeller, but his low finish was easily saved by the goalkeeper.
The situation on the pitch hardly changed after the break as Dortmund continued to have the upper hand. Surprisingly, its dominance bore fruit moments after the restart as in the 47th minute the reigning German champion was already in the lead.
A cross by Piszczek reached Kagawa on the right side of the box, and the Japanese international applied a skillful and powerful volley which hit the bar before ending up in the net as Rensing watched helplessly.
The 23-year-old attacker, however, did not stop there as he played a key role in Dortmund's third goal of the match shortly after. In the 52th minute the Japanese released Jakub Blaszczykowski with an outstanding backheel pass, who in turn squared for Lewandowski.
The striker easily converted from close range to make the score 3-1 in favor of Borussia Dortmund. After a 20-minute pause, the BVB juggernaut continued to tear apart Koln's defencse and Jurgen Klopp's men soon added a fourth goal.
A superb one-two between Kagawa and Gundogan split the Billy Goats' defence, allowing the Germany international to easily convert at the left post to pile more misery on the Stale Solbbaken's team.
Moments later, in the 80th minute, Kagawa was on target again poking home a cross by Piszczek to make it 5-1 for BVB. The rout was completed in the final minutes of the game by substitute Perisic, who slammed past Rensing to put the cherry on the cake.