Luca Toni opened the scoring for Bayern on 11 minutes, before a dramatic injury-time equaliser from Mladen Petric forced the game into extra-time.
Dortmund then had Jakub Blaszczykowski sent-off for a second bookable offence, before Toni slotted the winner on 103 minutes for the pre-game favourites.
Buckley had been starting at leftback for Dortmund in recent weeks, but had to be content with a place on the bench for the Final.
He entered the fray on 79 minutes when he replaced rightback Antonio Rukavina as Dortmund moved to a more attacking formation, and it appeared to pay dividends as they forced extra time.
But Toni’s eighth goal in just four games sealed an ill-tempered affair that saw 10 yellow cards dished out in front of 74 000 spectators at the Olympic Stadium.