Last season's champion was tied with opponent Dortmund heading into the weekend but forged a three-point gap — two clear of Sunday's (AEDT) early second-placed winner RB Leipzig – despite trailing to an effort from Marco Reus.
Bayern had lost Joshua Kimmich to injury with the game still goalless yet soon took the game away from BVB in clinical fashion either side of half-time at Signal Iduna Park.
David Alaba – the subject of some scrutiny amid failed contract negotiations – provided a swift riposte to the breakthrough goal, before Robert Lewandowski's 19th career strike against former club Dortmund secured a lead that substitute Leroy Sane stretched 10 minutes from time.
Erling Haaland belatedly found his shooting boots to set up a tense finale and Reus blazed a glorious opportunity over, while Lewandowski saw a late second ruled out for offside in a thrilling end to the match.
Lewandowski should have had his side in front within 41 seconds, instead lashing into the side-netting, before Roman Burki made an excellent two-handed save from Leon Goretzka's close-range header.
Haaland ran on to Gio Reyna's pass but directed a delicate finish across the face of goal and then looked to have been punished for his profligacy as Lewandowski took his second opportunity, only for a VAR (video assistant referee) review to highlight a marginal offside.
After Kimmich hobbled off – hurt in a lunge on Haaland that saw him booked – Reus hit Dortmund's 45th-minute opener, turning a smart effort past Manuel Neuer at the near post from Raphael Guerreiro's cutback.
But there was still time for Bayern to restore parity before the break as a set-piece routine allowed Alaba to shoot from 20 yards and earn a decisive deflection off Thomas Meunier.
Bayern then needed less than three minutes of the second half to lead as Lewandowski stooped to meet Lucas Hernandez's cross and head inside the right-hand post, although the same section of the goal frame then denied Kingsley Coman a quick third.
Ex-Schalke winger Sane arrowed in a fine low strike on the break to seemingly settle matters, but Haaland kept Hansi Flick's men on their toes as he stayed onside to round Neuer and lash into the net, a feat Reus could not repeat when he thundered his volley over.
That would prove Dortmund's last big chance, even as another VAR review robbed Lewandowski of a stoppage-time second.