Goals by Kroos in the seventh minute and Mueller in the 21st built a 2-0 lead. After Lukas Podolski scored for Arsenal in the 55th, Mario Mandzukic got Bayern’s final goal in the 77th.

The second leg of the total-goals series is in Germany on March 13.

“Let’s not hide the truth,” Arsenal manager Arsene Wenger said, “it will be very difficult. We will try to make the impossible possible.”

In Tuesday’s other game, Joao Moutinho scored in the 56th minute to give Porto a 1-0 win over visiting Malaga.

The first leg ends Wednesday when AC Milan hosts Barcelona and Schalke is at Galatasaray.

While Bayern leads the Bundesliga by 15 points and reached the Champions League final in two of the last three years — losing both — Arsenal is in the midst of the most trying season since Wenger was hired in October 1996.

Arsenal is fifth in the Premier League, 21 points behind first-place Manchester United and four back of rival Tottenham for England’s last berth in next season’s Champions League.

The Gunners, who haven’t won a trophy since the 2005 FA Cup, were knocked out by fourth-tier Bradford in December’s League Cup quarterfinals and were eliminated from the FA Cup’s fifth round by second-tier Blackburn last season.

Now this year’s Champions League title is a longshot.

“You have to give credit for their class,” Wenger said of Bayern. “In patches in the first half, there was a difference in quality.”

Arsenal central defenders Per Mertesacker and Laurent Koscielny had a poor night, with the first goal coming after Bayern collected an errant clearance from Koscielny. Mueller crossed for Kroos, who beat goalkeeper Wojciech Szczesny with an 18-yard volley.

Mueller scored when he poked the ball into an unguarded net after Szczesny parried a header from an unmarked Daniel Van Buyten.

Arsenal’s players were jeered when they walked off at halftime, while Bayern fans sang another rendition of “Football’s Coming Home” in English.

“We didn’t start great and that’s been a thing for us this season,” Arsenal midfielder Jack Wilshere said. “Maybe it’s a bit of nerves or anxiety because we show what we can do when we play.”

Podolski cut the gap when he headed Jack Wilshere’s corner kick into an open net. But Mandzukic finished a sweeping move by bundling in Philipp Lahm’s low cross at the far post, the ball looping up off the Croatian’s heel and beyond Szczesny.

“We are currently in astonishing form,” said Bayern coach Jupp Heynckes, who will be replaced by Pep Guardiola this summer. “Our quality is we can punish even the smallest mistakes of our opponents.”

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