Bayern dominated possession but failed to create many clear cut opportunities against their bogey team.
Bayern were dominant from the off and their first opening came from a gorgeous ball from Diego Contento to Franck Ribery but the Frenchman was foiled by Pedro Geromel who made the block.
Koeln's only sight of goal in the opening period came in the nineteenth minute when last week's goalscorer Taner Yalcin sliced a shot wide from just outside the box.
Three minutes later, a stray pass from Petit put Faryd Mondragon under pressure but the Bundesliga's oldest player gathered the ball in time under pressure from Miroslav Klose.
Klose had a disappointing afternoon and could only direct a flying header over the bar just before the half-hour after Ribery's cross.
The Frenchman tried to be a catalyst for his side and five minutes later he cut inside Miso Brecko but drilled a low shot into the side netting. A minute later he found Thomas Mueller in the center but the youngster could only toe-poke the ball wide of the goal.
In an encouraging spell for Bayern, Klose strode forward before striking from distance but Mondragon beat the ball away.
Toni Kroos began to have some joy down the right in the second half as Bayern laid siege. In the space of two minutes he found Bastian Schweinsteiger in the box after ghosting between two defenders before another excellent pass found Thomas Mueller who shot narrowly over from 20 yards.
Bayern remained on the front foot throughout and Koeln had Brecko to thank when the Slovenian made a vital clearance off the line from Daniel Van Buyten's header.
Koeln had late chances to steal the three points when Brecko turned Van Buyten one way and the other before his shot was beaten away by Hans-Joerg Butt. Then with eight minutes left, Butt spared his side's blushes when he saved from Petit.
It was not to be for the champions as, despite a late onslaught in which Faryd Mondragon produced a brilliant double save from Ribery and Mueller, they were made to pay for their profligacy.
Bayern travel next to Hoffenheim on Tuesday and Koeln have a trip to Mainz the same evening.
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