A red card for Laurent Koscielny at the start of the second half proved the turning point as Bayern came from behind to match their 5-1 scoreline from the first leg.
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Bayern are through to the UEFA Champions League quarter-finals for the sixth season running as Arsenal's faint flicker of hope for a famous comeback was extinguished in emphatic style.
The Gunners needed a minor miracle to overturn their 5-1 round of 16 first-leg defeat and, just for a moment after Theo Walcott pulled one back with the home side pushing hard for another, it was on.
Bayern weathered the storm, however, and once Robert Lewandowski had levelled from the spot after an incident that saw Laurent Koscielny sent off, the gig was up. Arsenal imploded and the visitors lined up to take advantage.
Ex-Chelsea man Arjen Robben marked his return to London with a goal before substitute Douglas Costa and Arturo Vidal capitalised on poor passes out of the back to make it 4-1. The pair then combined for a fifth as Bayern marched on.
Key player: Arturo Vidal
The Chilean usually rises to the big occasion and though Bayern struggled in the first half, he battled hard in the middle and popped up with two goals that completed a flattering victory for his team.
Clinical Bayern make it count ...
If Bayern weren't at their best, they were still able to come from behind to put five past Arsenal. Koscielny's red card and Arsenal's subsequent collapse both played a major part, but when the chances come, you still have to take them. Bayern did that expertly, just as they had done in the first leg.
... Arsenal fail to
It was ultimately in vain, but briefly it seemed it might be Arsenal's night – especially when the last-minute change, with Olivier Giroud replacing the ill Danny Welbeck, worked so well in the first half. The liberty it gave Alexis Sánchez, for one, gave the Gunners a different dimension. If only Arsenal had taken full advantage of that impressive first half.
Andy Brassell, Arsenal reporter (@UEFAcomAndyB)
A deflating end to what started as a very promising UEFA Champions League campaign, with an excellent group stage performance sending Arsenal through top of the pile. Arsène Wenger talked about "fine margins" in his pre-match press conference and so it proved – witness the short spell in which the Gunners were blown away in the first leg, and the small time between Giroud's near miss and the award of the penalty from which Lewandowski equalised.
Jordan Maciel, Bayern reporter (@UEFAcomJordanM)
Arsenal put on a brave display, but the task of overturning a 5-1 deficit was simply too great. Bayern were far from their best, but still walked off the pitch 5-1 winners on the night – that says a lot about their winning mentality.