Rafael Czichos set the tone for a miserable night from a Cologne perspective inside eight minutes.
The Billy Goats’ stand-in captain, who was deputising for an unwell Jonas Hector, misplayed a pass straight to Andrej Kramaric, who was denied an opening goal by a brilliant point-blank save from Timo Horn.
Bebou did manage to break the deadlock with around half-an-hour gone, the Togo striker collecting a precision-perfect Kramaric pass and firing home with aplomb.
Ex-Hoffenheim striker Anthony Modeste sent a tame header wide as the visitors went in at the break with it all to do.
Cologne's task was made a whole lot harder soon after the restart.
Christoph Baumgartner fashioned an opening for Kevin Akpoguma to pick out a cross. He did just that, whipping a telling ball into the danger zone for Bebou to flick in his second of the contest.
Baumgartner was on the receiving end of a David Raum cross to add a third barely 120 seconds later. Substitute Georgino Rutter set up Dennis Geiger for Hoffenheim's fourth with 16 minutes remaining.
The crossbar denied Kramaric a piece of the goal-scoring pie, before Stefan Posch added the gloss to a one-sided victory that takes Hoffenheim to within a point of Cologne in the top half.