Munich also leapfrogged Hoffenheim and Mainz 05 – who both played out draws to slip two points behind Bayern while Schalke 04 picked up their first victory of the season.
Munich did not wait long to strike, taking the lead after eight minutes with some fine passing.
Arjen Robben fed Thomas Mueller, who back-heeled to Mario Goetze and the youngster placed his shot perfectly inside the right post to make it 1-0.
Munich doubled their advantage in the 14th minute thanks to a powerful strike by Robert Lewandowski.
The champions took their foot off the gas but Goetze added his second goal in the 78th minute, pouncing on a loose ball in the box, before Mueller got his name on the scoresheet in the 85th minute to see Bayern to 11 points.
“We were well prepared for this game. We wanted to make good some things from the last match,” said Goetze, referring to Munich’s 0-0 draw last weekend at Hamburg.
– Heroics –
Hoffenheim missed their chance to keep pace with Munich but Jannik Vestergaard scored three minutes into injury time to secure a 3-3 draw at home to SC Freiburg and see them move on to nine points.
Mike Frantz scored in the 32nd and 33rd minutes for Freiburg. Tarik Elyounoussi pulled back a goal in the 44th minute and Sebastian Rudy equalised for Hoffenheim from a free kick after 63 minutes.
Freiburg went ahead as Vladimir Darida converted a penalty in the 75th minute. But the Czech international was sent off six minutes later, setting up Vestergaard’s heroics.
Haris Seferovic scored in the 82nd minute to secure a 2-2 draw for Eintracht Frankfurt at home against Mainz.
Jonas Hofmann gave Mainz the lead after 41 minutes and Shinji Okazaki grabbed his fifth of the season for the visitors in the 44th minute.
But Alexander Maier halved the deficit for Frankfurt a minute into injury time before Seferovic secured the point.
Schalke picked up their first victory of the season with a double strike early in the second half to beat Werder Bremen 3-0 on the road.
Max Meyer scored in the 48th minute and Roman Neustaedter doubled the lead in the 51st minute for Schalke and Tranquillo Barnetta made it 3-0 in the 85th minute.
“When things go bad, then everybody is criticised. But when things go well, then everything is okay. We played well and deserved to win this game,” said Schalke striker Klaas-Jan Huntelaar.
“We had a lot of pressure coming into the game. But we really played a strong second half,” said Schalke coach Jens Keller, who was without the suspended Julian Draxler and Kevin-Prince Boateng.
Bayer Leverkusen can jump from fifth to second on Wednesday when they host FC Augsburg.
Borussia Dortmund also play on Wednesday, at home against VfB Stuttgart, while Borussia Moenchengladbach welcome Hamburg, VfL Wolfsburg travel to Hertha Berlin and Hanover 96 host Cologne.