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 pass from Julian Brandt pass before pirouetting and firing a shot home.
Malen doubled up five minutes later, scoring for the fifth consecutive league match, before Hummels headed in a third just before 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.
Dortmund manager Edin Terzic said "we showed how well we can play today", but would not bite when asked if his side were on the way to a title.
"It was a really good step in the right direction."
Frankfurt manager Oliver Glasner lamented the home side's "brutal efficiency" and has now lost eight from eight against Dortmund.
Mainz 'knockout' Bayern
Bayern lost their lead atop the table after slumping to a 3-1 loss at Mainz, thanks to three goals in 14 minutes from the home side.
Mainz trailed 1-0 at halftime thanks to a first goal since October from Bayern's Sadio Mane, but hit back through Ludovic Ajorque, Leandro Barreiro and Aaron Martin.
Bayern have now won just two from seven since sacking manager Julian Nagelsmann for former Dortmund and Chelsea boss Thomas Tuchel in late March.
Speaking to German TV after the match, Tuchel said "they gave us a knockout", saying the side "had too much going on right now to fight back".
Tuchel said he would give his players three days off ahead of next week's clash against rock-bottom Hertha Berlin.
Mainz are now unbeaten in 10 league games and sporting director Martin Schmidt said he was "at a loss for words" to explain his side's form.
"It's unbelievable what the team is doing."
Bayern came into the match under heavy pressure, with the Bundesliga title the last trophy available after Wednesday's Champions League exit at the hands of Manchester City.
Mane, who sat out Bayern's last Bundesliga match through suspension following an altercation with teammate Leroy Sane, headed a Joao Cancelo cross past Robin Zentner for the opener after 29 minutes.
Mainz, who were coached by Tuchel between 2009 and 2014, fought back after the break, Ajorque heading in from close range after Yann Sommer failed to grasp a Lee Jae-sung shot.
A shellshocked Bayern, who had controlled the game until that point, looked disorganised and Mainz took advantage by grabbing the lead through Barreiro just eight minutes later.
Martin added another six minutes after that to seal Mainz's third straight league win over Bayern at home.
In the German capital, Marvin Ducksch struck a hat-trick as Werder Bremen deepened Hertha Berlin's woes with a 4-2 win on home coach Pal Dardai's return to the dugout.
Hertha brought back Dardai, who previously saved the club from relegation in 2021, last week but the Hungarian was unable to have an immediate impact.
First-half goals from Florian Kainz and Davie Selke set up a crucial 3-1 win for Cologne away at Hoffenheim, sending them 10 clear of the relegation places.
Wolfsburg romped to a 5-1 victory at Bochum, thanks to a double from Mattias Svanberg, along with goals from Jakub Kaminski, Patrick Wimmer and Luca Waldschmidt.
Winless in four, Bochum now sit just two points clear of the relegation spots.
