Pep Guardiola's men remain on track to emulate their achievements of last season, when the Bavarians won the Bundesliga, UEFA Champions League and DFB-Pokal, following a comfortable semi-final triumph at the Allianz Arena on Wednesday.
Midfielder Bastian Schweinsteiger put Bayern, who have already been crowned Bundesliga champions and won the FIFA Club World Cup in December, ahead midway through the first half with a fine headed effort.
Muller, who replaced Gotze in the Bayern starting XI following last weekend's 3-0 home defeat to Dortmund, came close to opening the scoring after eight minutes as his header from Schweinsteiger's clever cross was deflected against the crossbar.
The hosts laboured for much of the opening period against a determined Kaiserslautern defence, but Guardiola's men made the breakthrough in the 23rd minute when Schweinsteiger powered home a magnificent downward header from Arjen Robben's pinpoint corner.
And that lead was doubled nine minutes later, Kroos meeting Robben's lay-off on the edge of the area with an exquisite finish that curled past Kaiserslautern goalkeeper Tobias Sippel and into the bottom corner.
Bayern refused to take their foot off the gas, though, and would have added a fourth had Franck Ribery not missed the target when presented with an empty net from Muller's pull back.
The visitors then reduced the deficit on the hour mark, striker Zoller glancing Florian Dick's right-wing cross beyond Bayern goalkeeper Lukas Raeder.
But Bayern were far from finished and re-emphasised their dominance 13 minutes from time when Mandzukic confidently slotted home after latching on to substitute Gotze's throughball.
