The German giants found themselves two goals down in the tie with just over 15 minutes remaining but rallied to force the contest into extra-time before scoring twice in the additional 30 minutes.
Prior to the half-hour mark, the Italians were two to the good when Juan Cuadrado, on loan from Chelsea, received a quality pass after a confident run from Alvaro Morata before feigning to shoot in the area and then firing beyond Manuel Neuer.
The match rolled along with that 2-0 scoreline until the 73rd minute when Robert Lewandowski rose above his marker to emphatically head home Douglas Costa's cross from the right before a breathtaking equaliser early in injury-time from Thomas Muller.
Extra-time ensued and it was substitute Thiago Alcantara who edged Bayern ahead, playing a clever one-two with Muller, before rifling home.
And two minutes later, to rub further salt into the Juve wounds, teenage winger Coman produced a classy curling finish on his left foot to put his parent club out of Europe's elite club competition.
The triumph sees Bayern into the final eight where they have joinedReal Madrid and Atletico Madrid, Paris Saint-Germain, Manchester City, Wolfsburg, Benfica and Barcelona ahead of the quarter-final draw on Friday.
2015-16 UEFA Champions League - Round of 16 second leg
Bayern Munich (GER): 4 (Robert Lewandowski 73', Thomas Muller 90+1', Thiago Alcantara 108', Kingsley Coman 110')
Juventus (ITA): 2 (Paul Pogba 5', Juan Cuadrado 28')
*Bayern wins 6-4 on aggregate
Allianz Arena, Munich, Germany - 70,000