© Getty Images
Mario Gotze extended the defending champions' advantage just seven minutes later as Franck Ribery skipped past Joleon Lescott before crossing the ball in, where it eventually fell to Gotze for a close-range tap-in.
The Germans continued to look the stronger of the two sides, but a goal against the run of play from the returning David Silva got Manuel Pellegrini's side back into the game just before the half-hour mark, with the Spaniard sweeping it in from a James Milner header.
Silva's strike inspired the visitors, who finished the opening 45 minutes strongly, but they were unable to get back on level terms before the half-time whistle.
However, Joe Hart had to stop Bayern from restoring their two-goal lead just before the break, after Ribery tried to set up Gotze again, but the England international managed to parry the ball away.