Dortmund are on 51 points, more than any team in second place has ever had after 22 matches, but they are still eight behind Bayern, who won 3-1 against Darmstadt 98 on Saturday.
Dortmund, who have more points after 22 matchdays than 42 of the 52 Bundesliga champions had at that stage, are a massive 15 points clear of third-placed Hertha Berlin, who have 36.
"We were too wasteful with our chances for the 2-0 and then had a bit of luck in the end," said Dortmund coach Thomas Tuchel. "We were prepared for an intensive game. In the second half we controlled the spaces better and deserved the lead."
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It took them almost 45 minutes, however, to create a decent chance with Aubameyang firing wide from a good position.
Leverkusen responded with a chance of their own but Karim Bellarabi's shot was palmed wide by keeper Roman Buerki.
African player of the year Aubameyang struck in the 64th minute with Erik Durm delivering a fine cutback and the Gabon international tapping in for his 21st league goal this season.
The goal prompted an angry reaction from Leverkusen coach Roger Schmidt, who was sent to the stands by the referee, but refused to leave his technical area, causing the game to be briefly interrupted.
Referee Felix Zwayer stopped play and left the pitch until Schmidt followed his orders.
"That break was complicated and an advantage for Leverkusen," Tuchel said. "They could turn this negative situation for them and create a special energy in a very emotional stadium."
Leverkusen's Javier Hernandez should have grabbed an equaliser for the hosts in the 90th minute but the Mexican forward shot wide from close range with only the keeper to beat.
VfB Stuttgart substitute Martin Harnik scored a 74th minute equaliser at Schalke 04, salvaging a 1-1 draw that meant the home side missed the opportunity to join Hertha Berlin in third place on 36 points. Instead, Schalke now lie sixth on 34.
Hanover 96's chances of remaining in the top division received another hammer blow with a 1-0 loss to struggling Augsburg which leaves them anchored in last place on 14, four behind 17th-placed Hoffenheim.
(Reporting by Karolos Grohmann; editing by Toby Davis and Ian Chadband)
