Pep Guardiola's side had thumped Hamburg 8-0 and thrashed Paderborn 6-0 in their last two league outings, and it looked as though Cologne were on course for a similarly heavy defeat on Friday when Bayern went two up inside 10 minutes.
Bastian Schweinsteiger headed in from a corner in the third minute before Franck Ribery struck a fine individual effort, and Cologne fans could have been forgiven for fearing the worst.
However, the side with the second best away record in the league - behind only Bayern - rallied and halved the deficit through Anthony Ujah's header in first-half stoppage time.
Ujah had a golden chance to equalise shortly before the hour, but Manuel Neuer produced a fine save to preserve Bayern's lead, and the hosts pulled two goals clear again with Arjen Robben's header midway through the second period.
As Cologne pressed to get back into the game, they left themselves open at the back and Robert Lewandowski added a fourth with 15 minutes remaining to cap yet another dominant performance from the German champions.
Bayern applied early pressure and were in front inside three minutes as Schweinsteiger - back in the side as one of two changes - rose unchallenged to power in Robben's left-wing corner.
And Bayern did not have to wait long to make it two, as Ribery cut in from the left hand side and arrowed a low shot into the bottom left-hand corner from the edge of the box.
Another rout appeared to be on the cards but, on the stroke of half-time, Cologne pulled one back as Ujah leapt to head home Matthias Lehmann's right-wing cross.
The home side began the second half as they had the first, and Thomas Muller was wasteful in heading Rafinha's cross off target in the 55th minute.
Against the run of play, Cologne almost found an equaliser three minutes later when Slawomir Reszko broke free down the left and squared for Ujah, whose cushioned effort was superbly kept out by Neuer.
The Bayern goalkeeper had to be alert again from the resulting corner, diving to his right to parry substitute Marcel Risse's well-struck shot.
Bayern seemed stunned into action by those near misses, and restored their two-goal advantage in the 67th minute as Robben headed Ribery's chipped ball back across goal and just inside the far post.
The hosts then netted a fourth on the break as Robben crossed for Lewandowski, who was able to chest the ball in from practically on the line.
Robben and Mario Gotze both went close to making the final margin of victory more convincing, but in the end it mattered little as Bayern were able to celebrate the 115th anniversary of their formation in style.
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