The victory set a new European record of 14 consecutive wins across all competitions to start a season.
The Bavarians' triumph under the floodlights on Wednesday night eclipsed AC Milan's long-standing mark from the 1992/93 campaign. Bayern had equalled the Italian giants' 13-match streak with a 3-0 win at Borussia Monchengladbach last weekend, but their latest ruthless display ensured they now stand alone in history.
Bayern's success has been powered by their devastating front line. Harry Kane, who has already scored 22 goals in all competitions, continues to lead by example, while Luis Diaz and Michael Olise have added eight and seven respectively.
In total, Kompany's side have struck 51 goals and conceded only 10 during their record-breaking run, surpassing Milan's tally of 45 scored and 13 conceded in the early 90s.
In the DFB-Pokal clash, Bayern came from behind after Ragnar Ache gave Koln the lead in the 31st minute. Luis Diaz leveled the score five minutes later, tapping in the rebound from Josip Stanisic's shot, before Harry Kane put them ahead with a brilliant spinning finish assisted by Olise. Kane added his second after the break, and Olise sealed the win with a composed finish.
After the match, Kompany played down the significance of the record but praised his squad's mentality. "I don't really pay that much attention to these records," the Belgian told Sky Sport. "The records come when we approach every game with the mentality of wanting to win.
"The lads are fit, hungry, and you can see the quality in their movements. They want more, and that's helping us right now."
Bayern's relentless start has seen them sweep aside domestic and European opposition alike, building confidence ahead of their next major test. Kompany's men will look to stretch their streak even further when they host Bayer Leverkusen at the Allianz Arena on Saturday night.
Jonas Urbig has praised Bayern Munich's mentality and team spirit after playing a starring role in their 4-1 comeback victory over FC Koln in the DFB-Pokal second round on Wednesday.
Borussia Dortmund star Julian Brandt explained giving the captaincy to Nico Schlotterbeck in the loss against Eintracht Frankfurt in the DFB Pokal on Tuesday.
Borussia Dortmund secured their place in the DFB-Pokal round of 16 after a thrilling encounter with Eintracht Frankfurt, triumphing 4-2 in a penalty shootout following a 1-1 draw after extra time.
Bayern Munich sporting director Max Eberl has hailed Nicolas Jackson's growing influence after the Senegalese striker impressed in the club's recent Bundesliga victory over Borussia Monchengladbach.
