Juventus tested Bayern early with Andrea Pirlo going close with a customary free-kick which required a brilliant save from Manuel Neuer but Bayern provided more of the attacking threat and were almost ahead when Arjen Robben's effort striking the post with Gianluigi Buffon beaten early in the second half.
However, Mandzukic gave the Bavarians a handy three-goal lead just after the hour-mark when he was on hand to slot home after Buffon had marginally parried Javi Martinez's close range attempt.
That gave Bayern the real impetus but their second goal did not come until injury-time when substitute Pizarro received a ball from Bastian Schweinsteiger to slot home from the right side of the area sending the newly-crowned German champions into the final four.
2012/13 UEFA Champions League quarter-final - second leg
Juventus Stadium, Turin - 40,823