Harry Kane scored twice as Bayern Munich continued their perfect start to the new season with a 4-1 win at Cologne in the second round of the DFB-Pokal.

Vincent Kompany's side -- chasing a 14th successive victory in all competitions -- fell behind after 31 minutes when Ragnar Ache headed in from a corner.

Bayern, though, were soon back on level terms when Luis Díaz slotted in a rebound before Kane's improvised spin finish put them in front.

The England captain then powered in a header just after the hour to take his Bayern tally to 22 for the season and Michael Olise swept in a fourth.

Cheered on by a vocal home support at the RheinEnergie Stadion, Cologne had made a fast start.

Isak Bergmann Johannesson's rising shot was tipped over by Bayern goalkeeper Jonas Urbig, standing in for the suspended Manuel Neuer after his red card in last season's cup defeat to Bayer Leverkusen last season.

Kane then sent a header wide before Cologne winger Jakub Kaminski shot straight at Urbig.

Cologne took the lead in the 31st minute when Ache got up above Bayern defender Dayot Upamecano to head in from a corner, which was the first time Bayern had gone behind in any of their matches this season.

The Bavarian side, however, were back on level terms just five minutes later.

Defender Josip Stanisic drilled in a low shot from the left, which Cologne keeper Ron-Robert Zieler could only parry out and Diaz swept the ball back into the net.

Bayern then turned the match around in the 38th minute.

Olise played Kane into the right side of the penalty area, and the England captain spun back around his marker before clipping a left-foot shot back past Zieler into the far corner.

After the break, Diaz squandered a great chance to further extend Bayern's lead in the 52nd minute.

Kane sent the former Liverpool forward racing clear from inside his own half and clean through on goal into the penalty area with only Zieler to beat -- but the Colombian blazed his shot over.

Cologne, who sit eighth in the Bundesliga, were then almost level just before the hour when a quick exchange of passes put Eric Martel into the right side of the Bayern box and his low shot was palmed behind by Urbig.

Bayern eventually did get themselves a two-goal cushion when Kane powered in a close-range header from a corner on 64 minutes.

Olise added a fourth with 18 minutes left, after starting a break down the left before feeding Aleksandar Pavlovic. His pass to Diaz was laid off first-time for Olise to sweep the ball from the penalty spot.

Cologne substitute Linton Maina saw his late effort hit the post, with the ball bouncing safely back to Urbig as Bayern coasted into the last 16.