Mame Biram Diouf's late equaliser salvaged a point for the hosts to leave Dortmund without a win away from home this season.
Robert Lewandowski gave Dortmund the lead in the 26th minute before Diouf equalised four minutes from time.
Eintracht Frankfurt remain second, five points behind Bayern, despite a 2-0 defeat at Borussia Monchengladbach.
Juan Arango gave Gladbach the lead after eight minutes with a thumping long-range effort while Luuk de Jong made it two in the 24th minute.
Stefan Kiessling scored twice as Bayer Leverkusen came from behind to draw at Stuttgart.
Kiessling gave Leverkusen the lead after 13 minutes before Vedad Ibisevic converted a penalty to level the scores six minutes later.
Ibisevic fired his second in the 55th minute, but Kiessling completed a brace of his own to make it 2-2 just before the hour mark.
Leverkusen climbed to sixth while Stuttgart moved out of the relegation zone by earning their sixth point of the Bundesliga season.
On Saturday, Bayern Munich equalled their own Bundesliga record for consecutive victories at the start of a season thanks to a 2-0 success over Hoffenheim at the Allianz Arena.
Franck Ribery scored both goals to make it seven wins out of seven for the Bavarians, who are now just one win away from breaking a record they share with Mainz and Kaiserslautern.
Elsewhere, Felix Magath made an unhappy return to Gelsenkirchen as his Wolfsburg side were comfortably beaten 3-0 by Schalke.
Jefferson Farfan put the high-flying Royal Blues in front in the 33rd minute and goals from Ibrahim Afellay and Roman Neustadter in the second half earned them all three points.
Hamburg made it 10 points in their last four games with victory Greuther Furth, who slumped to their fourth home defeat.
Son Heung-min decided the game in the 17th minute with the Bavarians unable to find a response in a tense encounter.
Mainz also won 1-0 but they left it late to become the first side to beat Fortuna Dusseldorf in the Bundesliga this season.
Oliver Fink was shown a red card for the visitors in the 78th minute before Noveski struck five minutes from time to earn the hosts all three points.
Freiburg ended a two-game losing run to condemn Nuremberg to their fourth straight defeat with a 3-0 victory at the Dreisamstadion.
Cedric Makiadi's goal put the hosts in front in the 36th minute, before a penalty from Daniel Caligiuri and a late Marca Terrazzino strike wrapped up the win.
On Friday, Augsburg picked up their first win of the season with a 3-1 triumph over Werder Bremen.
Sunday's Bundesliga Results
Saturday's Bundesliga Results
Friday's Bundesliga Results