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The hosts had the first opportunity in the fourth minute when Javi Martinez beat the offside trap and found Arjen Robben. The Dutchman's angle was tight and his toe-poke was saved by the legs of Victor Valdes.
The deadlock was broken seven minutes later when Arjen Robben's arcing cross was met by Dante, who beat Daniel Alves in the air to head across goal for Thomas Muller to stoop low and nod it over the line.
Barca came close to equaliser minutes later when Pedro's low cross was turned just wide by Dante, with Lionel Messi waiting to pounce just behind.
As the half came to a close, neither keeper was again tested but Bayern forward Mario Gomez and Barca's young defender Marc Bartra were both cautioned.