Robert Lewandowski scored the only goal of the game to deny bottom side Cologne what would have been a memorable point and move the defending champions nine points clear at the top of the Bundesliga.
After Leipzig could only draw 1-1 away to Wolfsburg, Bayern knew that a win here would see them extend their seven-point lead at the top of the table. Having been rested for the weekend win at Frankfurt, David Alaba, Sebastian Rudy, Corentin Tolisso and Robert Lewandowski all returned to the starting eleven, meaning Joshua Kimmich, Javier Martinez, James Rodriguez and Kingsley Coman the men who dropped to the bench.
Cologne meanwhile, made two changes from the side that came agonisingly close to a first league win of the season on Sunday, with Tim Handwerker and Jorge Mere replacing Sehrou Guirassy and Konstantin Rausch.
And in a team hampered by injuries to fourteen first team players, it was 21-year-old right-back Lukas Klunter who was tasked attacking duties in the absence of any available strikers.
Bayern’s first chance would come twelve minutes into the match, Franck Ribery’s lofted ball found Thomas Muller in behind the Cologne defence, but goalkeeper Timo Horn charged down the effort from a tight angle, with the resulting corner coming to nothing.
Despite all their dominance of both possession and territory, it was an frustrating opening 25 minutes for the defending champions. Sule and Boateng both headed over from corners despite being unmarked, while Lewnadowski’s turn and volley from close range had neither the power nor placement to beat Horn in the Cologne goal.
For their part Cologne had a couple of half chances of their own, Klunter’s effort from the edge of the area was easily held by Starke in the Bayern goal, while Milos Jojic was unlucky not to be awarded a corner when his breakaway effort deflected behind off Alaba.
Arturo Vidal, Bayern’s matchwinner in Frankfurt at the weekend, was the next to go close 37 minutes in, flashing an effort across the face of goal from inside the area, and seconds later Muller was again frustrated by a tight angle as he headed into the side-netting.
For all Bayern’s efforts, it was Cologne who returned to the dressing room the happier of the two sides, as the injury-ravaged basement dwellers became the first side to stop Bayern scoring in the first half of a home league game since Schalke in April 2016.
Following the disappointment of that first half, Jupp Heynckes wasted no time in shaking up his Bayern side at the break, with Kingsley Coman and James Rodriguez sent on in place of Vidal and Tolisso.
It took Bayern just moments to squander their first chance of the second half, as David Alaba hacked an effort wide after bringing down Boateng’s cross little more than eight yards from goal.
Minutes later it was Lewandowski’s turn to send another chance begging, as he somehow managed head wide Muller’s fizzing cross from point-blank range. Minutes later the same combination would see the Polish striker volley well over from just outside the area.
Finally though, on the stroke of the hour, Bayern found their opener. A lofted pass from Boateng found the onrushing Muller, and this time Lewandowski was able to dispatch Muller’s cushioned header back into the bottom corner from six yards out, continuing his run of scoring in every home league game this season in the process.
The hosts very nearly doubled their lead five minutes later, as Boateng’s pinpoint pass was met by Coman, but his downward bounced agonisingly onto the bar, and Lewandowski was unable to follow up on the rebound.
Though Bayern’s onslaught continued, the floodgates refused to open. Rudy had a long-range effort that stung the fists of Horn before Lewandowski fired over while unchallenged after the ball fell kindly from a corner as the game entered the final quarter of an hour.
Five minutes from time James Rodriguez came the closest to doubling Bayern’s advantage, drifting inside before striking a curling that produced a flying save from the impressive Cologne stopper Horn.
Bayern were very nearly made to rue that miss minutes later, as the young Klunter did well to make space for a shot from the edge of the area, only for Starke to dive low and throw out a strong hand to deny the young defender turned attacker an unforgettable moment.
What had for so long looked like a training game for Bayern had almost ended in embarrassment, but the defending champions saw out those final seconds to continue what is already starting to look like a charge to yet another Bundesliga title.