Harry Kane's opener, an incredible curling strike on the turn, and a second-half header brought his tally to 22 goals in 14 games this season.

Wingers Luis Diaz and Michael Olise also got on the scoresheet for the 20-time German Cup winners.

Cologne's Ragnar Ache scored the opener, which put Bayern behind for the first time in a match this season.

Bayern's victory beat the record of 13 wins to start a season in all competitions set by Fabio Capello's AC Milan in 1992-93, the previous best mark in Europe's top-five leagues.

The in-form England captain Kane has scored two hat-tricks and six braces in Bayern's record-breaking run, only failing to score in two of 14 matches.

Earlier, Bayer Leverkusen scored two goals after the 120-minute mark to win 4-2 at a 10-man Paderborn.

A frustrating night for the 2024 German domestic double winners looked destined to go to spot-kicks until 19-year-old Ibrahim Maza netted to spare Leverkusen's blushes against their second-division opponents, who had not lost since August.

Aleix Garcia added gloss to the result with Cologne pushing for an equaliser.

Earlier, Alejandro Grimaldo's 60th-minute free-kick for Leverkusen -- his fourth dead-ball goal this season -- was cancelled out when Paderborn's Stefano Marino scored in the final minute of regular time.

In extra-time, Paderborn, who were reduced to 10 men before the hour for a last-man foul which led to Grimaldo's free-kick, stunningly took the lead through Sven Michel on 96 minutes.

But former Liverpool centre-back Jarell Quansah made it 2-2 shortly before the extra-time interval.

Winners in 2023-24, Leverkusen will be joined by current cup holders Stuttgart, who won 2-0 at Mainz thanks to goals from Luca Jaquez and captain Atakan Karazor.

Centre-back Jaquez rose high to head in a corner with six minutes gone. With 73 minutes played, Karazor blasted in on the counter after Germany midfielder Angelo Stiller's clever dummy fooled the home defence.

Former Liverpool goalkeeper Loris Karius endured an unhappy night as his Schalke side were thumped 4-0 by fellow second division side Darmstadt.

Wednesday's other winners Freiburg, Magdeburg, and Kaiserslautern join Borussia Dortmund, Hertha Berlin, RB Leipzig, Hamburg, St Pauli, Borussia Moenchengladbach, Holstein Kiel and Bochum in the last 16.