A dazzling run by Douglas Costa, after a perfect 40-metre pass from Xabi Alonso, saw the Brazilian power past Roberto Hilbert before he cut the ball into the box for Mueller to score in the 26th minute.
The hosts doubled their lead on the hour when the Germany forward grabbed his 76th league goal with a penalty. Dutchman Arjen Robben then made it 3-0 from the spot in the 71st.
“We played a very good game. We worked hard this whole week and they had just two chances in the game which is crazy,” Bayern coach Pep Guardiola told reporters.
Despite being without the suspended Jerome Boateng and his fellow central defenders Mehdi Benatia and Holger Badstuber through injury, Bayern were in complete control and could have added more goals with Leverkusen looking tired following their midweek Champions League qualifying victory over Lazio.
Both teams hit the woodwork in an exciting first half but the champions kept Leverkusen at bay in a one-sided affair after the break as the visitors lost in the league for the first time this season.
Bayern are two points ahead of VfL Wolfsburg and Cologne. Borussia Dortmund, on six alongside Leverkusen, Mainz and Ingolstadt 04, host Hertha Berlin on Sunday.
“We can play even better than today,” said Mueller. “When Douglas finds space he is a real weapon. Leverkusen go for the ball, they take risks, so you find the space.”
Cologne came from a goal behind as they scored twice in five minutes, including a controversial penalty, to beat Hamburg SV 2-1.
Anthony Modeste was adjudged to have been brought down by Bosnian central defender Emir Spahic, who was sent off, but television replays showed the Cologne player may have stumbled rather than been fouled.
Frenchman Modeste kept his nerve and converted his 80th-minute penalty, leaving Hamburg coach Bruno Labbadia fuming on the sidelines.
Bottom club VfB Stuttgart lost their third straight game, slumping to a 4-1 defeat at home to Eintracht Frankfurt, piling early pressure on new coach Alexander Zorniger.
To make matters worse Stuttgart were left with 10 men when keeper Przemyslaw Tyton received a straight red card in the 67th minute.
(Editing by Ed Osmond)