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Cologne surprised their visitors by taking the lead through Linton Maina after a counter-attack, finishing with a left-footed shot (41). Bayern Munich equalised thanks to Serge Gnabry following a pass from Frenchman Michaël Ulisey (45+5). They then regained the lead with a header from South Korean defender Kim Min-jae from a corner (71), and secured the victory through 17-year-old substitute Lennart Karl (84).
The match was halted for approximately eight minutes after kickoff due to the use of fireworks and smoke bombs.
This marks Bayern Munich's third consecutive win since the start of the new year, following a 5-1 friendly victory over Austrian side Salzburg and an 8-1 thrashing of Wolfsburg in the Bundesliga last week.
The team, coached by Belgian Vincent Kompany, has also secured their third consecutive league win since their 2-2 draw with Mainz in the 14th round.
Bayern maintained their unbeaten record in the league this season, achieving their 15th victory against two draws, raising their tally to 47 points in first place, 11 points ahead of Borussia Dortmund, who beat Werder Bremen 3-0 on Tuesday in the opening match of the round.