Teenager Toni Kroos, Simon Rolfes, from a penalty, and Eren Derdiyok gave Leverkusen a 3-0 lead against Nurnberg in only 34 minutes before Stefan Kiessling added the fourth with his sixth goal of the season midway through the second half.
Leverkusen, still unbeaten, have 20 points from eight games, three ahead of Hamburg SV who visit bottom club Hertha Berlin on Sunday.
Bosnia striker Edin Dzeko headed a 75th-minute equaliser as champions VfL Wolfsburg drew 1-1 at VfL Bochum while promoted Mainz 05 continued their impressive start with a 2-1 win at home to Hoffenheim.
Hannover 96, beaten 4-2 by Wolfsburg last week, were on the right end of a high-scoring match when they thumped promoted Freiburg 5-2.
Argentine forward Lucas Barrios scored his first league goal for Borussia Dortmund to give them a 1-0 win at Borussia Moenchengladbach, only their second of the season, in the day's last game.
Kroos, on loan from Bayern Munich, set Leverkusen on their way when he scored from a free kick in the second minute. The 19-year-old also won a 28th-minute penalty, converted by Rolfes, when he was fouled by Joahar Mnari.
Swiss striker Derdiyok added the third six minutes later after exchanging passes with Kiessling, whose headed goal in the 68th minute made him the Bundesliga's topscorer.
Bayern, missing injured Dutch winger Arjen Robben, dropped eight points behind Leverkusen as they failed to find the target against Cologne.
Louis van Gaal's team lost 1-0 at Hamburg a week ago and were held 0-0 at home by Juventus in the Champions League on Wednesday.
For the third match running, Van Gaal made the Bundesliga's most expensive signing Mario Gomez start on the bench, although he brought him on at halftime.
A frustrating afternoon for Bayern against unambitious opponents saw Bastian Schweinsteiger twice head against the crossbar in the first half.
Dzeko took his tally to five when he headed in Karim Ziani's cross to save Wolfsburg from a shock defeat at Bochum. His goal came two minutes after the hosts had Japan international Shinji Ono sent off for a high tackle on Josue.
Iran forward Vahid Hashemian had given Bochum the lead with a header early in the second half.
Mainz got off to a flying start against Hoffenheim as they scored twice in the opening 11 minutes.
Andreas Ivanschitz, surprisingly left out of Austria's squad again last week, volleyed home, then Burkina Faso striker Aristide Bance headed the second after a mix-up in the Hoffenheim defence.
Andreas Ibertsberger pulled one with three minutes left but it was not enough and Mainz pulled level with fourth-placed Hoffenheim on 14 points.