Serge Gnabry continued his remarkable scoring streak in London before Robert Lewandowski fired a late third.
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Serge Gnabry scored twice in four minutes and Robert Lewandowski added a third as the German team dominated at Stamford Bridge.
The match at a glance
Bayern were in the ascendant early on as Kingsley Coman ruffled the side netting and Willy Caballero had to dart from his line to thwart Lewandowski. The visitors went closest to striking before the break when Thomas Müller’s header clattered back off the bar though Chelsea offered a sporadic threat with Marcos Alonso testing Manuel Neuer with a low drive.
Hans-Dieter Flick's men were more clinical after the restart, however, and two goals in the space of four minutes underlined their control. Gnabry, who had scored four times at Tottenham on Matchday 2, grabbed another two in London by driving in from incisive Lewandowski passes.
Bayern's third goal was the pick of the bunch. Substitute Philippe Coutinho released the outstanding Alphonso Davies with a cute flick and his cross was buried by Lewandowski. Chelsea's disappointing night was confirmed by a late red card for Alonso.
Man of the Match: Serge Gnabry (Bayern)
Philip Neville, UEFA technical observer: "This was a match-winning performance from Gnabry with his two goals both ruthless finishes."
View from the stadium: Jon Phipps, Chelsea reporter
A forgettable night for Chelsea, whose UEFA Champions League hopes are hanging by the thinnest of threads. They just about held their own in a first half dominated by Bayern but it all unravelled in the space of five minutes. The needless booking for Jorginho, then two quick goals from Gnabry and it was game over. Lewandowski’s third put icing on the cake, and Bayern’s only disappointment will be that they did not score more.
Visitors' view: Jordan Maciel, Bayern reporter
Flick wanted his team to "make a statement" this evening and they did that and much more. Not only did they win but they did so in a fashion so dominant and so clinical that it was like watching one of the great Bayern teams of old. Gnabry was sensational once more on London soil as was Lewandowski, who shone more for his unselfishness than for his own goalscoring exploits. History tells us not to write Chelsea off but it would take a minor miracle for the German side not to reach the quarter-finals.
Frank Lampard, Chelsea manager: "The performance was poor and sometimes you have to be brutally honest. They outclassed us in every department and it's quite sobering. The level of team they are is why they challenge in the Bundesliga and Europe year in, year out. I'm disappointed we couldn't do more against them. We have to take it on the chin and work towards getting back to the levels we want to be at."
Serge Gnabry, Bayern forward: "Three goals should give us a lot of confidence. We need to be prepared for the second leg and we can't take it seriously enough. We saw last season with Liverpool beating Barcelona, we know we have to be careful and focus."
- This was Chelsea's heaviest home defeat in European competition
- All six of Gnabry's UEFA Champions League goals have come in London against English clubs, the other four being at Tottenham on matchday 2
- Bayern have scored two or more goals in all seven of their games in this season's UEFA Champions League
- Lewandowski is now the top scorer in the competition this term with 11 goals
- Bayern have hit 19 goals in their four away games in this season's UEFA Champions League
- Bayern are unbeaten in their last 13 UEFA Champions League away matches (W10 D3)
Chelsea: Caballero; Azpilicueta (Pedro Rodríguez 73), Christensen, Rüdiger; James, Jorginho, Kovačić, Alonso; Mount, Giroud (Abraham 61), Barkley (Willian 61)
Bayern: Neuer; Pavard, Boateng, Alaba, Davies; Kimmich, Thiago (Goretzka 90); Coman (Coutinho 66), Müller, Gnabry (Tolisso 85); Lewandowski