BVB advanced to within three points of leaders Bayern Munich as it earned an emphatic win over Stale Solbakken's side
Having received heavy criticism as of late, Shinji Kagawa responded positively as he put the hosts ahead after just seven minutes. Marcel Schmelzer made it 2-0 in the 25th minute, and Robert Lewandowski added a third moments before halftime, effectively putting the game out of reach through 45 minutes.
Five minutes after the break, Lewandowski made it 4-0, and captain Sebastian Kehl rounded off the win on 66 minutes as he headed home a fifth.
Kagawa's goal was the first real chance of the game, and the Japanese playmaker made no mistake as he slotted home with his first touch. Mats Hummels' ball over the top released Kevin Grosskreutz to spring the offside trap, and the winger cut back to Kagawa for the goal.
Schmelzer's second was a stunning finish from just inside the edge of the penalty area, as the Koln defense was caught napping. Following Mario Gotze's clever run, Sven Bender had his initial attempt blocked but managed to cut back to Schmelzer, who doubled the hosts' advantage.
On 44 minutes, Lukasz Piszczek spotted Bender streaking into the box, and the Germany international earned his second assist of the afternoon as he squared for Lewandowski to tap home from close range.
The hosts were in full control of the match from the opening kick-off, and could have been up by four or five goals at the break, but Michael Rensing made good saves to deny Grosskreutz and Kehl.
BVB picked up where it left off after halftime as Lewandowski burst into the box before slotting home a fourth. Later, substitute Jakub Blaszczykowski, who replaced Gotze at the break, latched onto Hummels' long ball and crossed for Kehl. The captain headed an emphatic goal, sealing the 5-0 result.
The result sees Dortmund move to second in the table, three points behind leaders Bayern Munich, who have a game in hand. The title holders are now two points ahead of their nearest competitors, Stuttgart, Bremen, and Monchengladbach. Koln, meanwhile, slips to 11th, with 13 points from 10 games.