Polish talisman Robert Lewandowski has been in red-hot form in front of goal as ever with 10 league goals to his name so far, although they do rely on him somewhat with next-highest scorers Arjen Robben, James Rodríguez and Corentin Tolisso all on just two league goals.
Three points separate the two heading into the game with Bayern top of the Bundesliga while Dortmund sit second - although that could all change come the final whistle. He is now the Bundesliga's top scorer. We can only be happy to be three points ahead after lying five points behind them.
After Aubameyang wasted his first chance of the match, Robben rounded off an exquisite Bayern move to give Bayern a 16th-minute lead.
The return of Jupp Heynckes in the Bayern dugout has done wonders for their performances as they boast six wins from six in all competitions since the German's arrival.
Bayern's victory was their seventh straight in all competitions since Heynckes took over last month following the departure of Carlo Ancelotti, while Dortmund are in complete free fall, suffering their third loss in their last four league games.
"We chose to play very compact, but that did not work in the first half".
RB Leipzig earlier climbed into second as they came from behind to beat Hanover 2-1.
"It was a match with a clear focus on attack", the former Borussia Dortmund striker said.
They beat Celtic in the Champions League on Wednesday night 3-0 to nearly secure their progress into the last 16 of the competition.
Winger Daniel Caligiuri scored the only goal against his old club.
Aaron Hunt put Hamburg ahead from a free-kick after a goalkeeping blunder by Ron-Robert Zieler, but Stuttgart levelled just after half-time when Daniel Ginczek converted a penalty. "The easiest way to do it is by winning a game again".
Mid-table Augsburg and Bayer Leverkusen shared the points in a 1-1 draw as Kevin Volland's strike just after the break was quickly cancelled out by Austrian defender Kevin Danso.