First-half goals from James Rodriguez and Robert Lewandowski gave Bayern a comfortable victory, their third straight league win under coach Jupp Heynckes, with Leipzig depleted after the 13th-minute dismissal of captain Willi Orban.
The Bavarians, who had edged past 10-man Leipzig on penalties in the German Cup second round on Wednesday, moved up to 23 points, three ahead of Dortmund, beaten 4-2 by Hanover 96. Leipzig, last season's runners-up, are third on 19.
"After the Cup battle on Wednesday we were once more very motivated and very well prepared," Bayern coach Jupp Heynckes told reporters.
"If you play with 10 after 14 minutes like Leipzig did then it is a major drawback but we did well to control the game and play smart football."
#We should have added another goal but it was more important to work well at the back," he said.
Bayern had possession from the start but their task was made much easier when Orban was dismissed with a straight red card for a last-man foul on Arjen Robben.
Only six minutes later Rodriguez drilled in for the lead and Lewandowski doubled it with his 10th league goal of the season although the Poland striker was then taken off injured.
The hosts stepped off the gas after the break but were never worried with toothless Leipzig, having taken top scorer Timo Werner off in the first half after the red card posing no threat.
Hannover forward Ihlas Bebou struck twice to hand them a 4-2 victory Dortmund, who are without a win in their last three league matches.
The 23-year-old Togo international twice out-sprinted the Dortmund defence and left the Ruhr valley club mired in a form crisis after a fine start to their campaign.
Peter Bosz' team have only one win in their last five matches in all competitions and despite twice coming back from a goal down could not stop Hanover's quick breaks.
VfL Wolfsburg notched their record-breaking sixth straight draw in the league under coach Martin Schmidt thanks to Divock Origi's stoppage-time equaliser against Schalke 04, with the match ending 1-1.
Schmidt became the first Bundesliga coach to draw his first six matches at a new club.
Hoffenheim lost 3-1 to Borussia Moenchengladbach for only their second defeat of the campaign as they dropped to seventh place on 16 points.
(Reporting by Karolos Grohmann; Editing by Ed Osmond)
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