The reigning champion saw its advantage halved when Borussia Dortmund beat Hoffenheim on Sunday (AEDT), but it did not look like remaining at three points once Corentin Tolisso opened the scoring at the Olympiastadion.
Thomas Muller doubled Bayern's lead before the break and, after a string of impressive saves, Alexander Schwolow gifted Leroy Sane a tap-in with a wayward pass across the face of his own goal.
Serge Gnabry added a fourth as the visitor's relentless pressure finally told in the closing 15 minutes, though Jurgen Ekkelenkamp lobbed home a consolation 35 seconds after being subbed on.
Tolisso had a goal ruled out for offside by the VAR in the second minute, with Schwolow making saves from Sane, Kingsley Coman and Robert Lewandowski to keep the game level midway through the first half.
After Ishak Belfodil threatened for the hosts, Tolisso stooped to head Coman's left-wing delivery into the bottom-right corner and give Bayern a deserved lead.
Tolisso missed an open goal and Schwolow kept out Lewandowski, but Bayern got their second on the stroke of half-time when an unmarked Muller guided Joshua Kimmich's free-kick home.
Suat Serdar was unable to hit the target from six yards out, and Bayern were out of sight when Schwolow's pass to Linus Gechter was intercepted by Sane, who was left with a simple finish into a vacant net.
Gechter did well to clear a looping effort from Gnabry off the line, but the winger was not to be denied again, drilling home a fine finish for Bayern's second goal in four minutes.
Dayot Upamecano had not even been on the pitch for a minute when he sold Manuel Neuer short with a back pass and, after the keeper thwarted Stevan Jovetic, Ekkelenkamp lofted in the follow-up to complete the scoring.