'We showed character and fought our way back into it both times,” said director of sport Christian Nerlinger.
At 17 years and 258 days, David is the youngest player ever to represent Bayern in the Champions League.
Leading scorer Mario Gomez faces a two to three-week lay-off after rupturing a calf muscle in Florence.
FCB fixtures, results, stats and links to match reports in the Bundesliga, DFB Cup and Champions League.
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