Bayern made a bright start to the game, and came close to breaking the deadlock with their first opportunity when Thomas Muller dragged an effort just wide of the post.
They wouldn't wait too much longer for the opener, though, as Mario Gotze fired home from close range in the 19th minute after Muller had volleyed the ball across the box.
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Timo Horn was twice forced to prevent Bayern from pulling further ahead in the first half as he blocked a tame effort from Muller, before reacting impressively to get a hand on Arjen Robben's low strike moments later.
Manuel Neuer joined his fellow goalkeeper in making a key contribution before the break, denying both Adam Matuszczyk and Anthony Ujah in the space of a few seconds when the hosts threatened to equalise against the run of play.
Koln continued to make life difficult for the visitors, but their chances of getting back into the game appeared slim as Bayern dominated possession in the early stages of the second half.
The champions doubled their lead with just over 20 minutes remaining when Daniel Halfar inadvertently put Robert Lewandowski's cross into his own net while under pressure from David Alaba at the back post.
It soon became a passing exercise for Bayern as they controlled the closing stages to safely secure all three points.