Bayern keep pace with Kaiserslautern win
The goals went in during the first half and from that point on Bayern never looked in any danger of slipping up. They missed further chances in the second half to improve their goal difference, but at least picked up all three points to keep them within two points of Dortmund.
Bayern opened the scoring in the fifth minute with a cross from Ribery to Gomez, who was left alone to turn and head the ball inside the near post.
The hosts went close to a second goal in the 23rd minute when David Alaba sent a free-kick over the wall but just inches wide of the post, with Kevin Trapp just watching and praying that the ball would go wide.
Mueller left Trapp without a prayer in the 30th minute as he beat the Kaiserslautern goalkeeper to the ball on the edge of the six-yard box to head in Bayern's second from Toni Kroos' free-kick.
As comfortable as Bayern seemed, Thanos Petsos did warn them not to take things too easily when he sent a volley just inches wide of the post just before the interval after they won their first corner of the match.
Gomez and substitute Arjen Robben both missed one-on-one chances against Trapp in the second half before Holger Badstuber's volley was saved by the Kaiserslautern goalkeeper.
The last chance came from Robben's free-kick which he curled over the wall but straight into Trapp's arms.