A double from promising youngster Thomas Muller and a goal apiece from German international midfielder Bastian Schweinsteiger and Frenchman Saer Sene saw Bayern to an ultimately easy victory over Milan.
The Italian side - whose lack of a big name signing has provoked the ire of their fans as they have seen Kaka and David Beckham leave - saw their only goal come courtesy of a howler by Bayern 'keeper Michael Rensing, who let a tame freekick from Andrea Pirlo slip through his arms into the goal.
Milan's Brazilian playmaker Ronaldinho - left out on Tuesday of the national squad for an upcoming friendly with Estonia - was at fault for Bayern's first goal as he lost possession in the centre circle and the hosts Uruguayan midfielder Jose Ernesto Sosa centred for Muller to shoot home.
The score remained the same till a crazy final 10 minutes saw four goals scored as first Schweinsteiger scored from 16 metres out with a low shot, then Rensing's blunder a minute later gave Milan some hope.
However, an increasingly exhausted Milan defence allowed Muller and Sene to round off a convincing victory in front of their French playmaker Franck Ribery, who was watching from the stands as he is suffering from tendinitis in the knee.
It left their demanding Dutch coach Louis van Gaal more than satisfied.
"I saw a good Bayern performance this evening (Wednesday), in terms of the style of play and in terms of their patience.
"We ran this match really well."
Earlier Manchester United had disposed of Argentinian side Boca Juniors 2-1.
United looked to have wrapped it up by half-time as they scored both their goals with Anderson scoring a superb first goal for them with a stunning freekick which taken from the right hand side went in at the far corner of the goal.
Recent multi-million pound signing Antonio Valencia added a second three minutes from half-time as he fired in a powerful shot, though, the Boca keeper should have done better as it was right at him.
The Argentinian side - who saw their league campaign along with all their rivals suspended earlier on Wednesday because of non payment of wages to players - came back strongly in the second-half inspired by playmaker Juan Roman Riquelme and deservedly got a goal back.
United hung on, though, and left manager Sir Alex Ferguson content if not overjoyed at their overall performance.
"I am happy with the way the match went, even if I wouldn't say that we played very well," said the ever demanding Scot.