Frankfurt have dumped Spanish giant, Barcelona out of the Europa League quarter finals on Thursday night.
In what was a dramatic game, Kostic gave Frankfurt the fourth-minute lead from the penalty spot after Eric Garcia pulled Jesper Lindstroem.
Santos Borre deservedly doubled their lead with a goal-of-the-tournament contender.
With a stunning left-footed strike into the corner midway through the second half, Kostic added a third, against the run of play.
Frankfurt wasted additional chances, giving Barca a chance to try a late charge.
In the 84th minute, Sergio Busquets had a goal disallowed for offside, but as the game entered injury time, the midfielder produced a scorching strike to set up a dramatic injury time finish.
Depay also converted awarded penalty after Memphis Depay netted a penalty in the 11th minute of added time to cut the deficit to 2-3, while visiting defender Evan N’Dicka was sent off for a second yellow card.