Croatian Rebic scored either side of a Robert Lewandowski equaliser and Frankfurt added a third in stoppage-time to make amends for last season's final loss.
It was a bittersweet farewell for Bayern's Heynckes, who will go back into retirement after taking over in October and leading them to their sixth straight Bundesliga title. Heynckes had coached them to the treble in 2013.
In a contrast of emotions, his Frankfurt counterpart Niko Kovac, who will take charge of Bayern next season, was lost in the arms of his players as he celebrated Frankfurt's first Cup win in 30 years.
"That's life," Kovac said. "I am happy for these amazing fans and for my team.
"When you stand together you can do everything. That is what marked this team for my two-and-a-half years here. Last year we missed out but this year we made it. We deserved it."
Bayern could have scored early when Lewandowski's free kick bounced off the crossbar but it was the underdogs who went in front when their pressing paid off in the 11th minute and Rebic was sent through to slot in.
Bayern squandered half a dozen golden chances through Bundesliga top scorer Lewandowski, Thomas Mueller and Joshua Kimmich before the break rescued Frankfurt.
Poland striker Lewandowski made amends in the 53rd, sliding in to drill home a Kimmich cutback.
The game had lost some of its earlier pace but Frankfurt again pounced on sloppy Bayern defending for Rebic to put them back ahead.
The Bavarians desperately searched for a late equaliser and hit the bar through Mats Hummels but they gave Frankfurt far too much space and Mijat Gacinovic found plenty of it to complete a break deep in stoppage-time and score into an empty net.
"We did not use our chances," Heynckes said. "In sports there are wins as well as defeats.
"Tonight was an avoidable defeat. But Frankfurt were ambitious, strong and with passion and they also had the necessary luck. They are deserved Cup winners," the 73-year-old added.
(Reporting by Karolos Grohmann, editing by Ed Osmond)
