Marco Reus headed home to conclude a superb first-half counter attack from Dortmund on Saturday - a perfect riposte from the visitors after talk this week of Bayern's interest in the Germany international had soured pre-match relations between the two clubs.
Dortmund goalkeeper Roman Weidenfeller then kept the league leaders at bay until Robert Lewandowski shot into the bottom corner to haul back his former employers.
Neven Subotic hauled down fellow substitute Franck Ribery to hand Bayern an 85th-minute penalty and Arjen Robben made no mistake, sending Weidenfeller the wrong way to win it.
Pep Guardiola’s team now hold a four-point lead at the summit, with Dortmund languishing third-from-bottom after their fifth consecutive Bundesliga defeat.
Bayern's closest challengers, Wolfsburg, stormed to a resounding 4-0 win over struggling Stuttgart.
A mix-up between Oriol Romeu and Antonio Rudiger allowed Ivan Perisic to give Wolfsburg a 15th-minute lead and Robin Knoche converted Kevin De Bruyne's free-kick in first-half stoppage time to double their advantage.
De Bruyne scored his fourth goal in as many games shortly after the restart and Perisic completed his brace two minutes from time to make it six victories in succession in all competitions for Dieter Hecking's men.
Hamburg lifted themselves out of the bottom three as Rafael van der Vaart's 26th-minute penalty secured a 1-0 triumph over Bayer Leverkusen, while Werder Bremen are now level on points with Dortmund thanks to their first win of the campaign, 2-1 at Mainz.
The home side took a third-minute lead as Shinji Okazaki latched onto Koo Ja-cheol's throughball to steer into the net right footed.
But Franco Di Santo nodded Bremen level a minute before the interval and the former Chelsea striker sealed the success five minutes later with a fine finish from an angle.
In Saturday's other game, Hannover moved level on points with fifth-placed Leverkusen as a late own goal from Eintracht Frankfurt defender Alexander Madlung proved to be the only strike of the match.
