Mueller now has five goals in the first three matches of the season — and 76 in the league for his career. Arjen Robben converted a penalty for his first of the campaign as Bayern put on a convincing display against one of the highest rated Bundesliga teams, which has qualified for the Champions League.
"We are getting along quite nicely," Mueller said.
Earlier, Yoshinori Muto scored his first pair of Bundesliga goals and set up one to lead Mainz past Hannover 3-0.
Cologne rallied to beat 10-man Hamburger SV 2-1, while promoted Ingolstadt and Darmstadt both picked up points in the Bundesliga.
Ingolstadt won 1-0 at Augsburg, which was last season's surprise team and qualified for the Europa League. Darmstadt earned its third draw in as many games, holding Hoffenheim 0-0. Eintracht Frankfurt won 4-1 in Stuttgart.
Last-place Stuttgart has lost all three games so far. Hannover is winless as well.
Leverkusen played polished, passing football but lacked the finishing punch and would have suffered a bigger defeat if Bayern had used all its chances, especially late in the match.
Because of injuries and suspensions, Bayern began the match without a single trained central defender but it allowed little openings to Leverkusen, which could not handle the speed of wingers Douglas Costa and Robben.
Costa sped past Roberto Hilbert and fed Mueller, who beat Jonathan Tah to the ball and knocked it in from close range in the 26th.
Costa struck the crossbar off a Robben cross, before Hakan Calhanoglu did the same on the other side.
Leverkusen began to tire in the second half and Hilbert pushed Arturo Vidal to give away a penalty, converted by Mueller in the 60th.
Robben also scored from a penalty, again given away by the hapless Hilbert, who handled the ball in the 71st.
"I am a team player," Mueller said laughingly, when asked why he did not take the second penalty as well. Robben had immediately signaled that he wanted to take the shot.
Hamburg defender Emir Spahic was sent off late in the match for pushing down Anthony Modeste and the striker converted the resulting penalty for Cologne's victory.
Stuttgart also finished with 10 men as Luc Castaignos scored twice.
Newly signed Muto, stepping in for Shinji Okazaki — who left for Leicester — scored the first two goals for Mainz inside the first 30 minutes and Yunus Malli completed the win early in the second half.
In Cologne, Hamburg scored the opening goal through Lewis Holtby in the 47th but newly signed Philipp Hosiner tied the match in the 76th.
Three minutes later, Spahic made slight contact with Modeste in the area and Cologne got the call. Modeste fired the ball in and Hamburg fell to its second defeat. Cologne has two wins and a draw.
Hamburg goalkeeper Rene Adler had to leave the match in the first half with a shoulder injury and Andreas Hirzel made his debut.
In Stuttgart, another goalkeeper got his Bundesliga debut when Odisseas Vlachodimos came on to replace Przemyslaw Tyton, who gave away a penalty and was dismissed in the 67th for clipping Castaignos.
Stuttgart, which like Hamburg fought against relegation last season, began strongly but fell behind on an own goal by Adam Hlousek in the 11th. Daniel Didavi leveled before Castaignos restored Frankfurt's lead for good. Haris Seferovic scored from the penalty before Castaignos completed the victory.