The Italians had grabbed an equaliser through Kroldrup before falling behind in the last minute of normal time.
Sadly the main talking points of the match will be the abysmal decisions of the officials who ultimately spoilt the game with a contentious red card and a clear offside which they failed to detect.
Fiorentina enjoyed a brighter first half creating the better chances. The Italians looked impressive going forward with Jovetic and Vargas probing at the suspect Bayern rearguard.
The Germans did attain the greater share of possession but lacked the cutting final ball to release Gomez or Muller up front and as a result rarely tested Frey in the Viola goal.
Their two expensive wingers had contrasting fortunes.
Robben looked lively and teased the away side with silky touches and delicate footwork. Meanwhile on the right Ribery looked off the pace and struggled to impact on the game as he continues his rehabilitation from injury.
Chances were few and far between in the opening period.
JoveticÃ¢â‚¬â„¢s corner was met by Cesare Natali who headed wide from just outside the six-yard box when he really should have scored.
Fiorentina continued to press and Riccardo Montolivo was next to unleash an effort at ButtÃ¢â‚¬â„¢s goal. But the Italian international, failing to control his strike, blasted his shot over the crossbar.
The first contentious refereeing decision arose when Bayern captain Mark Van Bommel lunged two-footed into a tackle on Montolivo. It was graphic challenge which the Danish referee, Tom Ovrebo, punished with just a caution despite having an unblocked view of the incident.
The Dutch international then escaped a second yellow despite dramatically diving underneath the nose of the referee, much to the fury of the Italians who demanded a second caution.
Chelsea fans will remember Ovrebo for his abysmal performance in the semi-final at Stamford Bridge last season. Unfortunately the dissatisfaction with his ability will have only intensified after this disappointing display.
The next talking point came when Robben was fouled in the box by Kroldup. Demichelis promptly rolled the ball into the gaping net coinciding with referee sounding his whistle and duly awarding a penalty. Ovrebo refused to allow the defenderÃ¢â‚¬â„¢s goal stand and insisted upon the spot kick being dispatched.
Robben stepped up and fired Louis Van GaalÃ¢â‚¬â„¢s team into the lead deep into stoppage time in the first half. It was cruel punishment for the visitors hailing from Florence who had played the better football and looked more dangerous in attack.
It took I Gigliati just five minutes to restore parity as the second period got underway.
When BayernÃ¢â‚¬â„¢s defence failed to deal with a corner, Kroldrup popped up to slide the ball past Butt. The Czech Republic defender made amends for his costly foul which had led to the first half penalty.
However the joy of the Italians was short lived. Left back Gobbi received a straight red for appearing to elbow Robben as the Dutch winger nipped past the defender.
On closer inspection it appeared that he had run into the motionless Fiorentina player, before falling to the ground clutching his throat. A caution was merited but a straight red was harsh treatment by the referee who was aided in his decision by the linesman.
The sense of injustice was merely heightened when KloseÃ¢â‚¬â„¢s high tackle on went unpunished just minutes later.
To make matters worse the officials made a further blunder which ultimately compelled the away side defeat despite a plucky performance.
The man advantage saw the Germans press for a late winner to ensure they made the trip to Florence with a slender aggregate lead. Die Rotten left it late, waiting until the 89th minute to snatch a dramatic winner.
Arjen RobbenÃ¢â‚¬â„¢s shot was parried by Sebastian Frey into the path of Olic. The forward nodded the ball square to his striker partner Klose who headed past the diving French keeper.
Replays showed that Klose was a clear three yards offside when Olic headed the ball into his path. The linesman stood in line with play but failed to raise his flag much to the frustrations of the Fiorentina playing and coaching staff.
The away team were furious but their protestation only ensured they made their way into the refereeÃ¢â‚¬â„¢s little black book.
If Michael Ballack or Didier Dorgba were watching they may have afforded themselves a wry smile, especially the German international at seeing his old club benefit from the shortcomings of the refereeing staff.
Bayern Munich: Hans-Jorg Butt,Ã‚Â Daniel van Buyten,Ã‚Â Martin Demichelis,Ã‚Â Philipp Lahm,Ã‚Â Holger Badstuber,Ã‚Â Franck Ribery, Arjen Robben,Ã‚Â Mark van Bommel,Ã‚Â Bastian Schweinsteiger, Thomas Muller,Ã‚Â Mario Gomez.
Fiorentina: Sebastien Frey,Ã‚Â Per Kroldrup,Ã‚Â Cesare Natali,Ã‚Â Massimo Gobbi, Lorenzo De Silvestri,Ã‚Â Juan Manuel Vargas,Ã‚Â Riccardo Montolivo, Mario Bolatti,Ã‚Â Marco Marchionni,Ã‚Â Stevan Jovetic,Ã‚Â Alberto Gilardin
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