The victory, courtesy of a sumptuous Joshua Kimmich goal just before half-time, moved them seven points ahead of second-placed Dortmund with six games remaining.
"It was brutally important,” said Kimmich of his 43rd minute strike that could bring a record-extending 29th top flight crown.
“I looked around to see if everyone understood how important it was.”
The significance of the slick chip over Dortmund goalkeeper Roman Buerk was not lost on Dortmund boss Lucien Favre.
Bayern favourites for title
“It will be difficult for the title now,” said the Swiss. “We played well for 90 minutes but we needed to be a bit more direct. We didn’t get enough shots on goal. Everyone knows that we miss our supporters.”
Ironically, a defensive midfielder settled a fixture billed as a shootout between Bayern’s goalmeister supreme Robert Lewandowski and Dortmund’s rising predator Erling Braut Haaland.
"Now only Bayern can decide what happens," said Dortmund skipper Mats Hummels.
"Sometimes, games are decided by brilliant moments and that was the case today."
