A goal inside the first minute from David Alaba set Bayern on the way and Thomas Muller added a second just after the hour mark as the German giant built a healthy advantage to take to Italy for the return leg.
However Bayern, runner-up in 2010 and again last year when it lost the final on home soil to Chelsea after a penalty shoot-out, will be wary of getting too confident.
In the previous round it beat Arsenal 3-1 away from home in the first leg but was then made to sweat for a place in the last eight after losing the home leg 2-0.
That was Bayern's only setback during a run of 13 wins in 14 matches coming into this game though, and on the weekend it moved to within one win of claiming the Bundesliga title with a 9-2 thrashing of Hamburg.
Confidence was flying and and it could hardly have had a better start against Italian title hopeful Juve at the Allianz Arena.
There were less than 30 seconds on the clock when Alaba picked up the ball 30 yards from goal before unleashing a left-footed effort which, after clipping the end of Arturo Vidal's boot, swerved past the hopelessly wrong-footed Gianluigi Buffon and into the bottom corner.
Juve might have felt a little unlucky to have conceded in that fashion but it could consider itself fortunate not to have conceded more during a first half that Bayern largely dominated.
After Juve playmaker Andrea Pirlo saw a dipping long-range free-kick land on the roof of Manuel Neuer's net, the home side started to create a number of good openings.
Substitute Arjen Robben, having replaced the injured Toni Kroos moments before, almost marked his introduction with a goal in the 18th minute only to be denied by a fine save from Buffon.
Franck Ribery then saw a shot deflected into the side-netting before Robben fired another great opening wide just after the half-hour.
Robben drew another save from Buffon in the 35th minute, albeit a comfortable one, before Bastian Schweinsteiger fired a half-chance over the bar.
Juve's best hope of success looked to be from Pirlo's set-pieces and it almost drew level from one on the stroke of half-time, Leonardo Bonucci glancing a header just over from the veteran playmaker's inswinging corner.
That effort, and the half-time interval, offered some respite to Juve but it was back on the defensive at the start of the second half, with Buffon denying Mario Mandzukic at his near post before then flying to his left to parry an Alaba free-kick.
Bayern was employing a shoot-on-sight policy and another effort from outside the box led to its second goal in the 63rd minute.
Buffon kept out Luiz Gustavo's shot but the rebound was picked up by Mandzukic and he laid the ball back into the centre for Muller to tap into an empty net.
Jupp Heynckes' side sensed it could all but finish Juve off before the second leg and Buffon needed to be alert to deflect away a thunderbolt from Ribery in the 70th minute.
Buffon then produced a superb one-handed save to deny Muller in the 90th minute and, with the Germany international firing the rebound over with the goal at his mercy, that could yet prove decisive in the second leg.