"Leverkusen played with 11 players and one of these players was Bernd Leno. When Leno is such an outstanding goalkeeper ..." Bayern coach Pep Guardiola said.
Mueller might have had a penalty in the second half, when he appeared to be pulled back by Omer Toprak, yet Bayern had ample other opportunities.
"I don't know. We did everything," Guardiola said. "Congratulations to my players. We're first in the table. I'm proud of our performance. We played very, very well. And that's football."
Bayern moved one point ahead of Dortmund, which is level with Leverkusen after eight games.
Dortmund dominated its game in Moenchengladbach but was dealt a blow when Mats Hummels was sent off after conceding a penalty by fouling Havard Nordtveit with 10 minutes to go.
Max Kruse scored from the spot a minute later, five minutes before Juan Arango set up Raffael to seal Dortmund's first defeat of the season.
"The defeat is down to our own stupidity," Dortmund winger Kevin Grosskreutz said. "'Gladbach have a very good team, which we dominated over 80 minutes. If only we'd scored."
Dortmund had 27 shots on goal compared to the home side's six, but failed to get past 'Gladbach goalkeeper Marc-Andre ter Stegen.
"The 2-0 was clearly undeserved after 90 minutes," acknowledged Moenchengladbach coach Lucien Favre.
Dortmund came one game short of equaling the club record of scoring in 32 consecutive Bundesliga games.
"Football can be unjust. We had to learn that at first hand today," Dortmund attacking midfielder Jonas Hoffman said.
Elsewhere, promoted Eintracht Braunschweig defeated Wolfsburg 2-0 for its first Bundesliga win in 28 years, Mainz came from two goals down to draw 2-2 with Hoffenheim, Schalke defeated 10-man Augsburg 4-1, and Stuttgart drew 1-1 at home with Werder Bremen.
Braunschweig's win at local rival Wolfsburg was its first top-flight victory since a 2-1 win at Bayer Uerdingen on June 1, 1985. This is its first season back in the Bundesliga.
"It's a very special day for the whole club," said Karim Bellarabi, who fired the visitors into the lead for the first time this season in the 31st minute.
Wolfsburg dominated possession but Domi Kumbela secured the result on a counterattack in the 86th.
"The pondering paid off this week," said Braunschweig coach Torsten Lieberknecht, referring to comments last week when he hinted at resigning after the 4-0 defeat at home to Stuttgart.
In Mainz, Hoffenheim striker Kevin Volland marched past five defenders before unleashing a shot beyond Heinz Mueller in the 14th, and Robert Firmino chipped the goalkeeper eight minutes later.
Mainz substitute Eric-Maxim Choupo-Moting pulled one back in the 82nd, before captain Nikolce Noveski secured an unlikely equalizer in injury time.
Bremen had Nils Peterson's 37th-minute goal to thank for canceling out Stuttgart striker Martin Harnik's sixth-minute opener.
Augsburg striker Sascha Moelders stunned Schalke fans in Gelsenkirchen when he fired the visitors ahead in the 10th minute.
But Kevin-Prince Boateng equalized with a penalty six minutes later, after Ragnar Klavan was sent off for hauling down Adam Szalai.
"Everyone saw the key moment of the game. We were very much in the game up to the sending off," said Augsburg coach Markus Weinzierl.
Szalai made it 2-1 in the 28th, when Roman Neustaedter sprung the offside trap and Atsuto Uchida set him up for a simple finish, and the Hungarian striker grabbed his second in the 78th, before Max Meyer wrapped it up in the 87th.
