Having surrendered the Bundesliga lead last weekend, the Bavarians scored twice in the first half courtesy of the two German internationals to ease towards a comfortable victory
Mario Gomez and Thomas Muller scored the decisive goals for the Bavarian giants, who stay within two points of leaders Dortmund with the win.
The hosts were at it from the off and took an early lead through Gomez in the sixth minute after the striker stole in at the near post to turn home Franck Ribery’s cross.
Bayern never looked threatened, and kept Kaiserslautern pinned back in their own half for the vast majority of the first half. Gomez went close once more, before David Alaba bent a free kick just wide of Kevin Trapp’s goal.
Perhaps inevitably, the home side doubled their advantage on the half hour mark. A free kick from Toni Kroos was aimed towards the head of Muller, who reached the ball just ahead of Trapp to nod the ball home.
The visitors fashioned a rare chance of their own from a corner five minutes before half-time, but Thanos Petsos could only volley wide of the far post.
However, that chance proved to be something of an anomaly, and Gomez had another chance five minutes after the restart when he raced through on goal, only to be stopped by the onrushing Trapp.
Two minutes later, Jerome Boateng saw a header cleared off the line by Kostas Fortounis after he was left completely unmarked following a corner.
Substitute Arjen Robben also saw himself twice denied by Trapp, who first stopped the Dutchman’s effort from a tight angle before blocking a more dangerous attempt by rushing off his goal line.
With 12 minutes left to play, Ribery and Holger Badstuber combined brilliantly in the middle of the park with the Frenchman releasing the centre-back on goal, but his volleyed effort was thwarted once again by Trapp.
There was still time for Robben to curl a late free kick into Trapp's arms, but the result had long been secured by that point.
Bayern stay two points behind Dortmund at the Bundesliga summit with the win, while Kaiserslautern remain third from bottom in the table, just one point ahead of Augsburg and Freiburg.