Robert Lewandowski has become the top foreign goalscorer in Bundesliga history.
Bayern could not be doing more to put pressure on Dortmund, who had been top since their sixth game of the season.
Dortmund returned to winning ways with a late 3-1 victory over Stuttgart, but Bayern are two goals better off with nine matches remaining.
Having been told on Tuesday, along with Bayern team-mates Jerome Boateng and Mats Hummels, that his Germany career is over, Mueller took out his frustration, setting up the first goal and scoring Munich's second. He will rarely have scored easier goals either as Serge Gnabry, who had given Bayern the lead, squared the ball for Lewandowski to slot home into an open goal.
And although Dortmund got back in front against Stuttgart, Kimmich and Lewandowski added late headers from Ribery centres to boost Bayern's more impressive goal difference further.
Marco Reus converted from 12 yards, but they needed Paco Alcacer and Christian Pulisic to seal the three points after Marc-Oliver Kempf had levelled for Stuttgart.
Substitute Pulisic settled Dortmund nerves in the 90th to lift his team to 57 points, level with Bayern, who went top after their 6-0 demolition of VfL Wolfsburg.
Despite some dogged Stuttgart defending, Dortmund took the lead at Signal Iduna Park when Reus netted a penalty on 62 minutes.
It was Pulisic's second goal of the season.
Also, Leipzig was held at home by Augsburg to 0-0, and Freiburg beat Hertha Berlin 2-1.
Champions for the last five years, Bayern have made up seven points on early pace-setters Borussia Dortmund and leapfrogged them on goal difference following a fine display at the Allianz Arena.