Germany striker Miroslav Klose put Bayern ahead after four minutes then midfielder Bastian Schweinsteiger scored a spectacular net-buster on 25 minutes before Brazilian Ze Roberto made it 3-0 on 90 minutes.
The three points meant Bayern top Group F with seven points, from second-placed Lyon on five, and puts the German giants in pole-position to reach the first knock-out phase, while Fiorentina are third in the table.
“The victory was very, very important and gives us lift, but we must build on this,” said a relieved Klinsmann. “We knew Fiorentina are a very strong, attacking team and had their chances to score a goal or two. We have to consistently reach that level and we hope we will just get better and better. I never doubted we would get to this level.”
But Bayern rode their luck against a spirited Fiorentina side as Azzurri forward Alberto Gilardino squandered two golden opportunities just after the break. And having picked up their first league win in four games last weekend, Bayern again showed they are weak in defence as goalkeeper Michael Rensing looked anything but secure on occasion.
“You can see again the Bayern defence is susceptible,” said Bayern president Franz Beckenbauer.
Bayern were still impressive in the first half as Bastian Schweinsteiger capitalised on a mistake in the Fiorentina defence to hit a fantastic long-range strike.
“It doesn’t get much better than that,” admitted an impressed Beckenbauer.
But with Romania striker Adrian Mutu and Azzurri hot-shot Gilardino in their ranks, Fiorentina failed to find the net despite 23 shots on goal – compared to Bayern’s 15 – which disappointed Gilardino.
“It is a disappointing result, Bayern were very strong in the first 25 minutes, but we wasted too many chances in front of goal which is disappointing,” said Gilardino. “This isn’t where we want to be in the table, but we still have to prove ourselves.”
With three games left for both teams there is still all to play for in the return leg on November 5 when the two sides meet at Fiorentina’s Artemio Franchi stadium.