Goals from Mario Mandzukic and Thomas Muller saw Pep Guardiola's side overcome Niklas Sule's 34th-minute opener for the hosts.
Bayern are now unbeaten in 36 Bundesliga games, matching the mark set by Hamburg between January 1982 and January 1983.
Dominick Kumbela’s 81st-minute strike proved decisive for Braunschweig, who had won just one of their previous 10 league fixtures.
Leverkusen's misery was compounded when fit-again Lars Bender, who signed a contract extension on Thursday, received a late red card for his second bookable offence.
Anderson Bamba's second-minute own goal gave Dieter Hecking's men an early advantage, but Alexander Meier levelled prior to half-time.
With a draw appearing likely, Maximilian Arnold struck in the 82nd minute to tilt the game in Wolfsburg's favour.
Adam Szalai's fifth goal of the season put Schalke ahead after 26 minutes and the Hungary international turned provider to set up Julian Draxler for a second deep into injury time.
In Saturday's other game, Freiburg recorded a 3-0 win at Nurnberg to climb above their fellow strugglers.
Both sides were seeking a first three-point haul of the season and a tight finish looked to be on the cards when Oliver Sorg was sent off for the visitors following Felix Klaus' 57th-minute opener.
