Bayern were ahead inside the opening minute when David Alaba found the back of the net from distance, but the German outfit missed a host of chances to extend their lead before the interval.
It was two for Bayern midway through the second period, however, when Thomas Muller converted from close range.
Here Sports Mole dissects the 90 minutes of action between the two European rivals.
On target: 9
On target: 2
Was the result fair?
There is not any possible situation where anything other than a Bayern win would have reflected the match this evening. However, it could and should have been by a more comfortable margin. The German outfit dominated the first leg from start to finish, but Juventus will still feel confident of turning things around in Italy.
Bayern Munich's performance
It is no exaggeration to say that Bayern could have been 5-0 ahead at the interval. Some of their attacking play was just delightful, with their forward players interchanging at each opportunity. That domination continued into the second half, although Juventus certainly improved in defensive areas. Once more they were impressive, but they do miss a lot of chances, which will be a concern.
This was just about as poor as Juventus have been this season. They arrived in Munich full of hope following an exceptional campaign to date, but they just did not get going. Andrea Pirlo was the pick of their players as he continued to pass and probe in the Bayern half, but the movement from his teammates was not there. The only positive aspect is that they are still in the tie.
Sports Mole's man of the match
Mario Mandzukic: Eyebrows were raised when Claudio Pizarro was dropped having scored four goals at the weekend, but Mandzukic was just stunning this evening. The Croatian won the aerial battle with Giorgio Chiellini, while his work-rate was of the very highest order. The only thing missing from his performance was a goal.
Biggest gaffe of the match
Bayern could have been out of sight in the first period following a host of clear chances, but they could not add to the scoring. It is difficult to criticise the German side having picked up a 2-0 win, but this tie should have been dead and buried following 90 minutes of pure one-way traffic.
Mark Clattenburg had a difficult evening with the challenges flying in from both sides. Bayern felt they should have had a penalty early on when Mandzukic was bundled over in the box, while Juventus midfielder Arturo Vidal was lucky to escape a booking for two poor challenges in the first period. However, he did rightly turn down a Juventus penalty appeal in the latter stages.
Bayern Munich: The German outfit will attempt to extend their lead at the top of the Bundesliga when they travel to Eintracht Frankfurt on Saturday.
Juventus: Juventus also return to domestic action on Saturday when they host basement outfit Pescara.