UEFA Update: Robben Wins Champions League For Bayern Munich
Dutchman Robben raced into the area and beat goalkeeper Roman Weidenfeller in a stunning finale.
Bayern, on the backfoot for much of the first half, struck on the hour with Robben cutting the ball back for Mario Mandzukic to poke home from close range.
The German champions' joy was short-lived though as Dortmund levelled eight minutes later with Ilkay Guendogan's well-struck penalty awarded for a clumsy Dante challenge on Marco Reus.
Dortmund looked to be holding on for extra time before Robben broke free to score the winner and send the Bayern fans into raptures.