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Dinamo looked dangerous on the break, and twice came close to finding the lead as Ulreich kept out an El Arbi Hillel Soudani effort, before the forward headed wide from a free kick on the stroke of half time.
After the break the visitors took control of proceedings, and could have taken the lead when substitute Thomas Muller hit a powerful effort on goal, only for Eduardo to deny the World Cup winner.
Bayern finally found the net on 61 minutes, when Muller picked out Lewandowski from the right, before the Polish striker headed past Eduardo.
The hosts came agonisingly close to pulling a goal back on 70 minutes, as Pivaric struck the woodwork after a strong run from left-back.
Lewandowski almost netted a hat-trick moments later, as Rode picked out the former Borussia Dortmund man, only for the Polish international to miss the target.
The visitors could have wrapped up the win with a third goal before the final whistle, when Eduardo brought Arturo Vidal down inside his own box. Muller stepped up to take the spot kick, and hit the post.body check tags ::