The Croatia international scored within minutes of his arrival off the substitutes' bench to ensure the defending champions retained their 100 per cent record in Group D.
The win means Bayern stay three points clear at the top of the table and are certain of a top-two finish after Manchester City beat CSKA Moscow in the group's other match.
Perhaps looking to exorcise the demons of their 5-0 hammering in Munich last time out, Plzen made a promising start with Michal Duris forcing an early save from Bayern goalkeeper Manuel Neuer.
Home keeper Matus Kozacik was then called upon to deal with a header from Thomas Muller, who was aiming to make the most of a helpful cross from Mario Gotze.
Kozacik also got his hands to a 25-yard free-kick from David Alaba soon after, but Bayern's best effort so far arrived after 16 minutes with a fierce shot from Bastian Schweinsteiger which pinged back off a post.
It was a wake-up call for Plzen, who responded with a long-range drive from Frantisek Rajtoral which was high of the target.
Bayern then began to crank up the pressure and Kozacik had to be at his best to turn away shots from Schweinsteiger, Franck Ribery and Toni Kroos as the European champions looked to gain an edge.
Plzen were not without their chances though, and Duris pumped a cross into the area which was headed narrowly over by Tomas Horava as half-time approached.
The German visitors quickly reasserted their authority after the interval and a one-two with Muller almost paid off for Philip Lahm, whose goalbound shot was swept off the line by Marian Cisovsky.
Daniel van Buyten then put a header inches wide of the right post following a Ribery corner, while the Frenchman decided to go it alone after 56 minutes only to see his angled effort saved by Kozacik's feet.
Pep Guardiola's growing frustration resulted in a double substitution on the hour mark, with Javi Martinez and Mandzukic coming on for Schweinsteiger and Muller.
And the move paid off six minutes later when the Croatian forward met a cross by Lahm to the far post, planting a header just beyond the reach of Kozacik.
Plzen responded to the challenge facing them and Neuer preserved his side's advantage after 74 minutes with a save at full stretch to deny Duris.
Moments later, Milan Petrzela whipped a cross from the right into the area but it was just beyond the toes of Stanislav Tecl, who had the goal at his mercy.
Pavel Horvath also fired wide of the left post as the final minutes approached but an equaliser would not come and Bayern almost nicked a second in stoppage-time with Lahm's half-volley palmed away by Kozacik.