Arsenal midfielder Jack Wilshere toils without Bayern Munich's supporting cast

England midfielder was the stand-out performer for the home side

The Emirates Stadium

How better to respond to humiliation at home than to treat everywhere else as your patch?

Bayern Munich came to north London yesterday as the best travelling side in the game, and showed exactly why. This was a remarkably proprietary performance, in which Bayern exerted confidence and control and ownership while Arsenal, the home team, nervously scrambled and scrapped for slivers of opportunity.

Bastian Schweinsteiger, the thumping heart of this team, said in the build-up that the defeat in last year's final provided a "huge" motivation this year. Of course it did. Bayern are a very proud team and yet they were soft and profligate in allowing Chelsea to snatch the European Cup from them in their own Allianz Arena. Could a worse blow to Bavarian esteem be imagined?

"A defeat like that you just can't forget it," Schweinsteiger said on Monday afternoon, "but you have to think about it and deal with it." Bayern, a club where walk matches talk, have done precisely that. This season in the Bundesliga, which Bayern are strolling, they have conceded just one goal away from home, and seven in total – by far the best record in Europe.

Tonight it was very easy to see why. Bayern played just how you would expect them to do back in Munich. They pressed from the front, with Franck Ribéry and Thomas Müller either side of Mario Mandzukic. There was no question of waiting to break when the game was already there to be won. The Arsenal back four was put under pressure and started to gift them back the ball.

With Bayern's front three playing like that, there was inevitably space for Toni Kroos to drift into just behind. There was much pre-match discussion of Jack Wilshere, and he played well, but Kroos – a similar player, a few inches taller and two years older – was probably superior. Kroos played with the touch, vision and awareness of space that seems to be inherent in young German midfielders as a matter of course.

From the first minute Arsenal could not live with Kroos' movement, lacking yet again a territorial enforcer in front of their back four. It was next to no surprise, then, when eight minutes in Kroos drifted to the edge of the box, received Müller's cross and volleyed past Wojciech Szczesny to put Bayern ahead. They could have scored a second even sooner than they did when Kroos shuffled in between Mikel Arteta and Per Mertesacker to win a free-kick which came to nothing.

But Wilshere can do that too and the difference between them might have been what was behind them. Wilshere was supported by Arteta and Aaron Ramsey, decent players but, unlike him, not of Champions League calibre. He had to spend too much of the evening going backwards to help them out and win the ball back.

Kroos had no such concerns. Behind him was Schweinsteiger and Javi Martinez, as efficient, powerful and refined engine-room duo as there is outside of Barcelona. This is not a pair of complimentary styles but one where both are serious all-rounders, adept at tackling, turning, passing and running. Schweinsteiger has always been dynamic, but Martinez, who arrived from Bilbao in the summer, has turned into a Basque Michael Ballack in a matter of months, such is the authority of his strut.

With control like that, Bayern hoarded the ball, waiting for overlaps, and they soon scored a second. Philipp Lahm gave them an option and won the corner which Kroos took and Müller converted.

Only when they had scored those two away goals were Bayern happy to take half a step back, confident in their own powers of containment. Arsenal, as they do, grew into a game which they had already lost, but Bayern might point to the fact that Lukas Podolski's goal came from a corner which should never have been awarded.

When Bayern looked like they needed something new from the bench, they were able to add Arjen Robben, who is a rather useful player to have in these or any other circumstances. He had something to contribute too, playing Lahm in for another overlap, and the cross was bundled in by Mandzukic at the far post.

The Bayern fans were understandably delighted, singing in perfect audible English "Football's coming home". Of course, club football offered to come back to Munich last May and Bayern somehow blew their chance. This year the final is only a few miles away from the Emirates, at Wembley Stadium.

It is more than possible that Bayern will be there on 25 May. They will, it can safely be said, be in the quarter-finals. There are teams who could beat them there or in the semi-finals, but no-one they will fear too much. They certainly do not look like they will be rattled on their travels any time soon.

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