With extra time beckoning, Robben collected a back-heel from Franck Ribery, eluded the challenge of Mats Hummels and rolled a delicate shot past Roman Weidenfeller to give Bayern their fifth European crown yesterday.
It was a moment of long-awaited deliverance for both Bayern and Robben after defeats for the Bavarians in the final of the competition in 2010 and again in 2012, when they cruelly lost a penalty shoot-out to Chelsea on home soil.
Victory made Bayern coach Jupp Heynckes only the fourth manager to win the trophy with two different clubs after a 1998 triumph with Real Madrid, as he prepares to step aside for incoming successor Pep Guardiola.
Having already claimed the German title, Bayern will now look to complete an unprecedented treble by beating VfB Stuttgart in the German Cup final next weekend.
"First of all, congratulations to Bayern, as they won. After the game you have to respect the result," said Klopp.
"We deserved to be in the final. We showed this tonight. That is not the most important thing but it is important."
The player who had generated the most column inches in the weeks leading up to the game was in the stands at kick-off, a hamstring injury having denied Mario Goetze a farewell appearance for Dortmund before his 37 million euros (�31.7 million, $47.8 million) move to Bayern.
