Juventus are aiming to win their fifth successive Serie A title, something they last did in the 1930s.
Mario Goetze came off bench and scored Bayern’s second goal in the 79th minute.
Real were missing the firepower of their regular attacking trio with Ronaldo and Benzema out injured and Bale on the bench.
Bayern struck back with second-half goals from Lewandowski and Mueller but it was a case of too little too late.
Barcelona have the 3-goal advantage going into the second leg at Allianz Arena on Tuesday.
Bayern goalie Neur was earlier quoted in an interview saying that he would show Messi who the boss is.
Bayern Munich is currently struggling to field 11 players with Ribery, Robben, and Martinez ruled out.
Bayern Munich are unbeaten in all competitions this season and are already through to the last 16 of the CL.
Arjen Robben is doubtful for the season opener against VfL Wolfsburg due to lack of match practice.
Dortmund beat Bayern 2-0 in German Super Cup on Wednesday to win the first domestic title of the season.
Bayern Munich will not sign any more players during the current transfer window despite a series of injury setbacks.
Extra-time goals by Robben and Mueller help beat Dortmund as Munich complete domestic double.
Victory ended a bad run for Bayern, who had a slump in form, including a comprehensive CL semis defeat by Real Madrid.
Pep Guardiola said it’s up to the club to decide whether he’s the right coach or not.
Ramos, Ronaldo doubles give Madrid 4-0 win over Bayern, shot at 10th European title.