The German and European champions eased past Augsburg at home 3-0 thanks to first-half strikes by Jerome Boateng and Franck Ribery, followed by a disputed Thomas Muller penalty in stoppage time.
Victory meant a 37th league game without defeat for Bayern, surpassing the mark set by Hamburg in 1983.
That feat tasted sweeter still for Pep Guardiola's men after closest rivals Borussia Dortmund lost 2-1 despite taking the lead at Wolfsburg.
Marco Reus put Jurgen Klopp's team ahead with a curling free-kick on the stroke of half-time, but Ricardo Rodriguez's speculative effort and a magnificent winner from experienced striker Ivica Olic means Dortmund will return from the international break to host Bayern four points in arrears.
On the day they lost a proud Bundesliga record, Hamburg came out on the wrong side of an eight-goal thriller at third-placed Bayer Leverkusen as they lost 5-3.
Heung-Min Son was Leverkusen's hat-trick hero, with Stefan Kiessling and Gonzalo Castro also getting in on the act as the hosts drew level with Dortmund on 28 points.
Maximilian Beister and Pierre-Michel Lasogga brought Hamburg level at 2-2 and the latter's second of the match set up a grandstand finish before Castro settled the issue.
Bottom club Nurnberg remain winless following a late collapse at Borussia Monchengladbach.
Josip Drmic coolly slotted the visitors ahead but Juan Arango equalised 18 minutes from time with a superb, curling 25-yard strike in to the top corner.
Niklas Stark then put through his own net from Arango's free-kick and Patrick Herrmann completed the scoring.
A Kevin-Prince Boateng brace helped Schalke to a 3-1 win over Werder Bremen. Jens Keller's side are sixth – one place and two points better off than Hertha Berlin, who edged to a 3-2 triumph at Hoffenheim thanks to an Adrian Ramos double.
