Marco Reus, who struck with an audacious back heel after just two minutes, Sokratis Papastathopoulos and Pierre-Emerick Aubemayang were all on target after the Dortmund fans gave their players a rousing reception back at the Westfalenstadion.
Second-placed RB Leipzig made sure they will play in the Champions League for the first time next season after a handsome 4-0 win over Freiburg put them on to 61 points, seven clear of Hoffenheim.
Hoffenheim beat Borussia Moenchengladbach 5-3 to stay a point clear of fourth-placed Dortmund, remaining on course for a best-ever Bundesliga finish and also a maiden Champions League berth.
Their cause was helped by defeat for fifth-placed Hertha Berlin who went down 1-0 at lowly Mainz.
A tumultuous week for Dortmund quickly took a turn for the better in the opening minutes of the game against Frankfurt.
Their opening goal came after a slick one-two with Aubameyang finding American teenager Christian Pulisic, who used his pace to catch Eintracht goalkeeper Lukas Hradecky in no man's land. The American kept his composure to find Reus in front of goal for a stunning back-heeled finish on his return from a month out with injury.
Eintracht had two good chances before Mexican Marco Fabian equalised only for a right-footed shot from Papastathopoulos to restore Borussia's lead 10 minutes before half-time.
Aubameyang grabbed his 26th Bundesliga goal of the season to seal success in the last five minutes.
The players had been greeted by a stirring reception from their supporters at a packed stadium with a visible extra police presence.
Read the full article on eurosport.co.uk: Dortmund win at end of traumatic week, RB Leipzig claim Champions League spot