A brace from Ante Rebić either side of a strike from Robert Lewandowski had put the Eagles into a shock lead with just seconds left on the clock.
And after surviving a late claim for a penalty, which even went to VAR, Frankfurt's Serbian midfielder Mrjat Gaćinović ran the length of the pitch before putting the icing on the cake in Niko Kovač's last game in charge of the club - he will succeed the retiring Heynckes at the Allianz Arena this summer.
"If you lose you don't have to talk about the referee," Heynckes said after the game, quoted by Bayern's official website. "I have to congratulate Eintracht on the cup victory. We made a mistake in our build-up play which resulted in the opener, we were a bit unlucky when Robert Lewandowski's free-kick hit the bar.
"Our opponents stuck to their play, they're resolute, aggressive and very hard-running, so we have to accept the result.
"Frankfurt displayed a boundless will to win the final. It was an avoidable defeat. If you don't take your chances you shouldn't be surprised to lose a final like this."
Bayern Munich will now be looking to build for life withough Heynckes in charge of the club, and Kovač offers the Bavarians an exciting long-term successor to their legendary manager.