A double from Dutch forward Donyell Malen and goals from English teenager Jude Bellingham and veteran Mats Hummels snared the three points for Dortmund, setting up a knife-edged title race with five games remaining.
With Bayern's game finishing an hour before kickoff in Dortmund, the home side knew a win would take them outright first on the table.
Bellingham settled Dortmund's nerves early, collecting a Julian Brandt pass before pirouetting and whacking the ball in.
Malen doubled up five minutes later, scoring for the fifth consecutive league match, before Hummels headed in a third in the shadows of halftime.
Malen scored his second midway through the second half, again assisted by Karim Adeyemi.
Unlike last week, where Dortmund gave away 2-0 and 3-2 leads against a ten-man Stuttgart to draw 3-3, there would be no late collapse as the home side leapfrogged Bayern into first by one point.
Dortmund have five more matches, three of which are at home, as they pursue their first league title in a decade.
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