The Croatian striker opened the scoring midway through the second half before substitute Claudio Pizarro added a second right at the death
The Bavarians soaked up what little the Bianconeri could throw at them during the early exchanges of both halves before eventually putting the outcome of the tie beyond all doubt when Mario Mandzukic converted from close range just after the hour-mark.
Juventus tried to rally but there was to be no way back for Antonio Conte's game but limited side, who were opened up again in the dying seconds when substitute Claudio Pizarro fired home.
While the Bianconeri had to make do without suspended duo Arturo Vidal and Stephan Lichtsteiner, they were at least buoyed by Mirko Vucinic’s return to full fitness, with the Montenegrin having been restricted to the role of substitute in Munich.
Unsurprisingly, a fired-up Vucinic was particularly prominent early on, curling a tame strike into the arms of Manuel Neuer before then lofting the ball into the path of Claudio Marchisio, who drove forward with will menace only to then blaze high and wide as the Bayern goal came into range.
Bayern, though, weathered what was a very early and a very brief storm, and it took an expertly executed sliding challenge from Simone Padoin to prevent Mandzukic from finishing off a terrific move down the right-hand side involving Arjen Robben and Franck Ribery.
Andrea Pirlo lifted the home fans with a stinging free kick from the edge of the area that Neuer did well to fist over the bar, while Paul Pogba flashed a ball across the face of the six-yard box that criminally went unconverted.
However, for all the Bianconeri’s bluster, and the loss of Daniel van Buyten to injury 35 minutes in, Bayern looked reasonably comfortable and they arguably finished the half the stronger, with Gianluigi Buffon having to produce a flying save to keep out a well-struck drive from David Alaba.
Vucinic, though, put Juve back on the front foot with a barnstorming run right at the heart of the Bayern back-line immediately after the interval and, just moments later, strike partner Fabio Quagliarella flashed a shot just wide of Neuer’s right post.
However, the increasingly desperate hosts unsurprisingly began to leave holes at the back and one brilliant Bayern breakaway on 57 minutes really should have resulted in the opening goal, Mandzukic deftly laying the ball off into the path of Robben, who took a touch before striking the post with a sublime curling effort from 20 yards out.
The Bavarians’ disappointment did not last long, though, with Mandzukic on hand to convert the rebound after Buffon had done brilliantly to keep out Javi Martinez’s point-blank range volley from a Bastian Schweinsteiger free kick.
The visitors should have doubled their advantage moments later but Thomas Muller blazed over after being put through by Robben. However, Bayern would get the second goal their dominance deserved when Pizarro slotted home after slipped in by Schweinsteiger to put the seal on another statement of intent from a side clearly driven by their desire to atone for last season's defeat by Chelsea.